(a) The growing rate of shadow when the person is 30 ft from the lamp post is 15/7 ft/m
(b) The moving rate of the tip of the shadow when the person is 30 ft from the lamp post is 50/7 ft/m
Given,
Height of the man = 6 ft
Height of the lamp post = 20 ft
[tex]\frac{dx}{dt} =5 ft/m[/tex]
Let,
The distance between the base of lamp and the man = x
From the geometry,
[tex]\frac{6}{20} =\frac{y}{x+y}[/tex]
[tex]6(x+y) = 20y[/tex]
[tex]3x=7y[/tex] .......................(1)
And,
[tex]6(\frac{dx}{dy} )=14(\frac{dy}{dt} )[/tex]
[tex]\frac{dy}{dt}=\frac{15}{7}[/tex]
∵ [tex]\frac{dx}{dt} =5 ft/m[/tex]
∴ [tex]\frac{dx}{dt}+\frac{dy}{dt} =5+\frac{15}{7}[/tex][tex]=\frac{50}{7}[/tex]
Hence,
(a) The growing rate of shadow when the person is 30 ft from the lamp post is 15/7 ft/m
(b) The moving rate of the tip of the shadow when the person is 30 ft from the lamp post is 50/7 ft/m
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Suppose a rocket is fired vertically upward from the surface of the earth with one-half of the esacpe speed. How far from the center of the earth will it reach vefore it begins to fall back?
(let g = 9.8 m/s^2 and Re = 6370 km)
A. 1.3 * 104 km
B. 8.5 * 103 km
C. 9.6 * 103 km
D. 2.6 * 104 km
E. 1.9 * 104 km
The correct answer: B.
I do not understand why I am not getting the correct answer.
The distance before it falls back to the earth is 8.5 * 103 km. Option B
What is the escape velocity?We know that the escape velocity has to do with the velocity that has to be supplied to a material so that the material can be able to escape from the earth's gravitational pull. Let us recall that the whole earth is a large gravitational field. If we throw an object up then the object would have to certainly fall doen to the ground under the influence of gravity.
It is therefore clear that gravity is the force that draws any object that goes upwards down back to the ground. Given that we have been told here that the speed is one-half of the escape speed, then then the magnitude of the speed is 5590.3 m/s.
Given that;
v^2 = u^2 - 2gh
v = final velocity
u = initial velocity
g = acceleration due to gravity
h = height
Then;
u^2 = 2gh
h = u^2/2g
h = ( 5590.3)^2/2 * 9.8
= 8.5 * 103 km
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in the figure, light is incident at angle on a boundary between two transparent materials. some of the light travels down through the next three layers of transparent materials, while some of it reflects upward and then escapes into the air.
(a) θ5 in the air is 56.9° and (b) θ4 in the bottom material 35.30°. Normally, a light beam that strikes an angle on a prism's refracting face emerges from the opposite face.
How to calculate?(a) Approximating n=1 for air, we have
n1. sinθ1 = (1)sinθ5 ⇒56.9°=θ5
and with the more accurate value for n air in Table below, we obtain 56.80.(b) Equation n1 sinθ c =n2 sin 90° leads to,
n1 sinθ 1=n2 sinθ2 =n3 sinθ 3 =n4 sinθ 4
so that. θ4 =sin −1( n1/n4.sinθ 1 )=35.30° .
What does angle of incidence mean?The angle of incidence is formed by a line drawn perpendicular to the reflecting barrier and the wave's direction of motion.
Is the incidence angle of refraction?Refraction Depending on the Refractive Indices in the Two Media and the Angle of Incidence. Snell's law states that the angle of incidence, I and the proportion of the refractive indices of the two media that make up the interface determine the angle of refraction, r.
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A bowling ball accidentally falls out of the cargo bay of an airliner as it flies along in a horizontal direction. As observed by a person standing on the ground and viewing the plane as in the figure below, which of the paths 1-5 would the bowling ball most closely follow as it falls to the ground.a. 10
b. 2
c. 4
d. 45
4th paths out of 1 - 5 would the bowling ball most closely follow as it falls to the ground
The bowling ball moves due to the resultant force of the vertical and horizontal direction.
What is resultant force ?The overall force operating on the item or body as well as the direction in which the body is moving are referred to as the resultant force. When the object is stationary or moving at the same speed as it, there is no consequent force.
The outcome is what is produced when vectors are added together. The biggest (maximum) consequent when adding two vectors is equal to their sum when forces are acting in the same direction.
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During the heating season, a damper in the bypass duct is closed to prevent air from passing through the humidifier. Electronic humidistats are equipped with solid-state sensors in place of a hygroscopic element. Evaporative humidifiers contain an element that is kept damp. False
This statement is False because Solid-state sensors are used in place of a water - absorbing element in electronic humidistats. A damper in the bypassed duct is closed during the summer period to stop airflow.
What is hygroscopic and example?Hygroscopy - A material is said to be hygroscopic if it has the capacity to adsorb and retain water or water from its immediate surroundings. Examples include ethanol, glycerin, concentrated sulfuric acid, honey, silica gel, and methanol.
How hydroscopic is water?Around the soil particles, some water in the soil creates an incredibly thin, firmly held layer. It's referred to as hydroscopic water. A little amount of water in the soil is chemically linked to soil components in the soil. We refer to it as mixed water.
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Two blocks, with masses indicated in the figure above, are at rest on a horizontal surface and connected by a string of negligible mass and a compressed spring. There is negligible friction between the blocks and the surface. The string is cut, and the spring pushes the blocks away from each other. Which of the following statements are true about the motion of the blocks immediately after the string is cut? select two answers.
1. The velocity of the center of mass of the two-block system is zero.
2. The magnitude of the acceleration of the left block is greater than that of the right block.
The center of mass, or balancing point, of a distribution of mass in space is the only location where the total of the weighted relative positions of the distributed mass equals zero. In order to accelerate linearly without also accelerating angularly, a force might be applied at this moment. Using the center of mass as a reference point simplifies calculations in mechanics quite a bit. To imagine how an object would move, one can imagine a hypothetical location where the object's total mass is concentrated. To apply Newton's equations of motion to a particular object, the center of mass is the particle equivalent of that thing.
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9. What is the mass of a sky diver falling at a velocity of 52 m/s who has a kinetic energy of
97344 Joules?
Answer: m = 72 kg
Explanation:
A wire is formed into a circle having a diameter of 20.0 cm and placed in a uniform magnetic field of 2.50 mT. The wire carries a current of 5.00 A.
(a) Find the maximum torque on the wire.
_____ µN·m
(b) Find the range of potential energies of the wire-field system for different orientations of the circle.
minimum
_____µJ
maximum
_____ µJ
The maximum torque on the wire is 392.3 µN·m and the range of potential energy is -392.3µN·m(minimum) to +392.3µN·m(maximum)
Torque: Torque is a measure of the force that can cause an object to rotate about an axis. It is a vector quantity.
Given that,
diameter D=20cm
Radius r =10cm
magnetic field B =2.5mT
current I=5A
Torque= n×B
=nBsinФ
torque=nB= NIAB
= 1×5×π×[tex]10^{2}[/tex]×[tex]10^{-4}[/tex]×2.5×[tex]10^{-3}[/tex]
= 39.23×[tex]10^{-5}[/tex]
= 392.3µN·m
minimum potential energy= -nB= -392.3µN·m
maximum potential energy =+nB= +392.3µN·m
Therefore the maximum torque on the wire is 392.3 µN·m when is placed in an uniform magnetic field of 2.50mT and the range of potential energy is -392.3µN·m(minimum) to +392.3µN·m(maximum)
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Can someone help me and tell me as soon as possible
Answer:
copy and complete this diagram so that the system is in equilibrium
A pulley system is used to lift up a 90N boulder. What is the mechanical advantage if you only need to use 15N of force to lift the boulder?
By simply creating more loops or pulleys, the pulley system's mechanical advantage can be accomplished.
Equation:
It is known that a pulley system can lift a crate with 90 newtons of force. Finding the pulley system's mechanical advantage is important if the input force is 15 newtons.
The force makes the distance longer as though it were working. Mechanical advantage is not greatly affected by the number of pulleys. This is only based on the amount of weight that needs to be lifted.
Therefore,
F1/F2 = 90/15
F1/F2 = 6
Given that the crate's weight is 90 N and the input force is 15 N, this makes sense.
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Calculate the power of an electric bulb which consumes 2400 J in a minute
power of the bulb = 40 watt
Briefing
Power: In physics, the term "power" refers to the rate at which a task is completed, or how much energy is used during the allotted time.
What is energy now?
In physics, energy refers to the ability to do a task. It may exist in different forms, including potential, kinetic, thermal, electrical, chemical, radioactive, and others.
Consequently, in light of the posed query:
2400 J of energy
60 seconds in a minute is time.
As a result, we know that Power = Energy/Time.
p = E/t p = (2400-/60) joules/sec
p=40 W
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apply the loop rule to loop 2 (the smaller loop on the right). sum the voltage changes across each circuit element around this loop going in the direction of the arrow. remember that the current meter is ideal.express the voltage drops in terms of vb , i2 , i3 , the given resistances, and any other given quantities.
The voltage drops in terms of vb , i2 , i3 , the given resistances, and any other given quantities.ΣΔV = 0 = I3 ⋅ R3 - I2 ⋅ R2.
When applying Kirchhoff's second rule the loop rule we need to identify closed loops and decide whether to loop clockwise or counterclockwise. For example, in Figure 3 the loop was traversed in the same direction as the current.
Loop 1 is the full loop and Loop 2 is the small loop on the right. To apply the loop rule, add all those voltage changes. Kirchhoff's Second Law, also known as Kirchhoff's Voltage Law states that the sum of all voltages around the closed loop of any circuit must be zero. This is a result of charge conservation and energy conservation.
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A single loop of copper wire lying flat in a plane, has an area of 7.80 cm^2 and a resistance of 2.70 Ω A uniform magnetic field points perpendicular to the plane of the loop. The field initially has a magnitude of 0.500 T, and the magnitude increases linearly to 3.50 T in a time of 1.10 s. What is the induced current (in mA) in the loop of wire over this time?
The induced current in the loop of the copper wire is found to be 7.85 mA.
The single loop of the copper wire is lying in flat plane and the magnetic field is pointing perpendicular to the plane of the loop. The area of the loop is given to be 7.8cm²
The magnetic field initially has a magnitude of 0.500 Tesla and it finally increases manner to grow to a magnitude of 3.50 Tesla in a time 1.10 seconds.
The induced EMF in the circuit will be given by the relation,
E = A∆B/∆T
Where,
B is magnetic field,
A is the area and T is the time taken.
Putting all the values,
E = 0.00078×(3.5-0.5)/1.1
E = 21.2mV.
The resistance in the copper loop is given to be 2.7 ohm.
Now, the induced current in the circuit will be given by the relation,
I = E/R
Putting all the values
I = 21.2/2.7
I = 7.85 mA.
So, the induced current in the wire is 7.85 milliamps.
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A roller coaster starts from rest at point A. If you ignore friction and take the zero of potential energy to be at C, A) the kinetic energy of the coaster at D will be equal to its potential energy at A. B) the kinetic energy of the coaster at E will be equal to its potential energy at C. C) the kinetic energy of the coaster at C will be equal to its potential energy at A. D) the kinetic energy of the coaster at B will be equal to its potential energy at C E) None of these is correct. 13. Two objects are sliding at the same speed across a wooden surface. The coefficient of kinetic friction between the first object and the surface is twice that between the second object and the surface. The distance traveled by the first object before it stops is S. The distance traveled by the second object is A) impossible to determine without knowing the masses involved. B) 28 C) S/2 D) S E) 4S 14. A person of weight w is in an upward-moving elevator when the cable suddenly breaks. What is the person's weight measured in the elevator immediately after the elevator starts to fall? A) w B) greater than w C) less than w D) 9.81w E) zero A force F produces an acceleration a on an object of mass m. A force 3F is exerted on a second object, and an acceleration 8a results. What is the mass of the second object? A) 3m B) 9m C) 24m D) (3/8)m E) (8/3)m 15.
A roller coaster starts from rest at point is option C) the kinetic energy of the coaster at C will be equal to its potential energy at A.
Since Two objects are sliding at the same speed across a wooden surface. The distance traveled by the second object is option B) 2S
A person's weight measured in the elevator immediately after the elevator starts to fall is option E) zero A force F produces an acceleration a on an object of mass m.
The mass of the second object is option D) (3/8)m.
What happens when kinetic energy is equal to potential energy?The amount of kinetic energy change and the amount of potential energy change are identical in all physical processes that take place in closed systems. When the kinetic energy rises, the potential energy falls, and vice versa.
Wave speed is the number of meters a wave travels in a second, or the distance a wave travels in a particular amount of time. Equation Speed = Wavelength x Frequency describes how wave speed relates to wave wavelength and wave frequency.
Therefore, When wavelength and frequency are known potential energy stored energy that depends on the relative positions of different components of a system may be utilized to compute wave speed—this equation can be used to determine wave speed. When stretched or squeezed, a spring has higher potential energy.
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a wire of length l is wrapped into a coil with n turns this coil is then placed in a magnetic field of strength b
Maximum torque developed is (BIL²/4[tex]\pi[/tex]n).
Torque is a measure of force that can cause an object to rotate about an axis.
A force causes an object to accelerate in linear kinematics. Similarly, torque causes angular acceleration. Torque can therefore be defined as the rotational equivalent of a linear force. The line about which the object rotates is called the axis of rotation. In physics, torque is simply the tendency of a force to rotate or twist.For any structure such as a solenoid, toroid, and circular arc, the magnetic field at a certain point of the structure is always proportional to the number of turns of the coil.
As we know magnetic field is (BIL²/4[tex]\pi[/tex]n)
2[tex]\pi[/tex]rn = L
r = (L/2[tex]\pi[/tex]n)
A = [tex]\pi[/tex]r²
A = (L²/4[tex]\pi[/tex]n²)
M = niA
M = (iL²/4n[tex]\pi[/tex])
Then Torque is Z = MBSin90°
The question is incomplete, the complete question is "a wire of length l is wrapped into a coil with n turns this coil is then placed in a magnetic field of strength b, the maximum possible torque developed is?"
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what should be the value of 'x' such that the mass то exerts a force of mg on the inclined surface at P. (N=mg)
The value of 'x' such that the mass то exerts a force of mg on the inclined surface at P. (N=mg) is given by
x = N / (mg cos θ)
What is value of 'x'?Generally, To determine the value of 'x', you need to know the angle of inclination of the surface and the mass of the object. The force of gravity (N) acting on the object is equal to the mass of the object (m) multiplied by the acceleration due to gravity (g). The force of gravity is also equal to the normal force (N) exerted by the surface on the object, which is perpendicular to the surface.
If the surface is inclined at an angle θ with respect to the horizontal, the normal force will be equal to the component of the force of gravity along the surface. This component can be calculated using the formula N = mg cos θ, where θ is the angle of inclination and m is the mass of the object.
Therefore, to determine the value of 'x', you need to solve the equation N = mg cos θ for 'x'. To do this, you can rearrange the equation to solve for x:
x = N / (mg cos θ)
Substituting the values of N, m, and θ into this equation will give you the value of 'x' that you are looking for.
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The smoke from the Old Man’s furnace travels up from the basement at a velocity of |.5 meters per second. Ralphie is sitting in the kitchen above and can smell the smoke within 6 seconds. What is the approximate distance that the smoke travels up from the furnace?
The approximate distance that the smoke travels up from the furnace is 9metres.
What is distance?Distance is described as a numerical or occasionally qualitative measurement of how far apart objects or points are. In the field of physics or everyday usage, distance is usually referred to a physical length or an estimation based on other criteria.
Parameters given:
Velocity = 1.5
time = 6 seconds
We know that distance = speed x time
Hence, distance = 1.5 x 6 seconds
distance = 9 meters.
Distance is a scalar quantity that refers to how much ground an object has covered in the course of its motion while we can describe displacement as a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.
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for a severe supercell ts to form over the great plains, one would expect the 5,000 agl wind to be group of answer choices 360/10 kt 200/15 240/90 190/45
Note that for a severe supercell ts to form over the great plains, one would expect the 5,000 AGL wind to be 190/45kts (Option D)
What is a supercell?A supercell thunderstorm is distinguished by the presence of a mesocyclone, which is a deep, continually revolving updraft. As a result, these storms are sometimes known as spinning thunderstorms.
Supercells are storms that have updrafts that spin along a vertical axis and are generally but not always thunderstorms. This rotation is caused by shear in the environmental wind field (a change in wind direction and/or speed with height) that surrounds the storm as it grows.
Supercell thunderstorms are intense, long-lived storms that are characterized by strong wind shear and rotational dynamics.
The wind shear, or the change in wind speed and direction with height, is a key factor in the development and maintenance of supercell thunderstorms.
Note that AGL means Above Ground Level; while
KTS means Knots. Knots are a unit measurement of speed. I nautical mile is usually equated to one knot.
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A rod has a length 2.0000m at 20.0C. The length of the rod increases to 2.0005
5.00 × 10-3/K is the coefficient of thermal expansion of the material from which the rod is made as it increases its length to 2.0005m
What is the purpose of the thermal expansion coefficient?The coefficient of thermal expansion explains how an object's size varies when temperature changes. In particular, it measures the fractional size change per degree change in temperature at constant pressure, where lower coefficients denote a reduced propensity for size change.
What does thermal expansion mean?The propensity of matter to alter shape, volume, and area in reaction to a change in temperature is known as thermal expansion. The average molecular kinetic energy of a substance has a monotonic relationship with temperature.
How is thermal expansion calculated?Use the equation for linear thermal expansion ΔL=αLΔT Δ L = α L Δ T to calculate the change in length, ΔL .
How to solve?Get your rod hot enough to achieve, say, 1% linear thermal expansion.
The rod's dimension has increased to 1.01 units.
The rod is 1.030301 times its original size, or 1.013 larger than it was before heating.
This equals 1.03 when rounded to three major figures. In other words, its volume is 3% higher than that of the cold specimen.
The linear expansion is tripled, or 3%, by the volumetric expansion.
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Complete question:
A rod has a length 2.0000 m at 20.0°C. The length of the rod increases to 2.0005 m when the temperature increases to 40.0°C. What is the coefficient of thermal expansion of the material from which the rod is made?
Elcft parallelepiped is in an electric field which to the left of the dashed line; has the value Eleft =< -55.37,0,0 > N/C,and Eright =< 55.37,0,0 > N/C to the right of the dashed line_ The top and bottom of the parellelepiped are rectangles Iying in the = plane, and measure /1 by l2, as shown: The left and right faces are rectangles inclined by an angle 0 = 83.489 from the € axis, and measure lz by l3. The values Of L1,l2, and l3 are 23.82 cm, 11.27 cm, and 32.48 cm, respectively. What charge is contained inside the parallelepiped?
There is a net flux going into the surface, the parallelepiped must have a net charge (negative charge). Additionally, without an external field, all lines would point at the slab.
Six parallelograms come together to form a three-dimensional shape called a parallelepiped (the term rhomboid is also sometimes used with this meaning). It is comparable to a parallelogram in the same way that a cube is comparable to a square. There are three similar descriptions of a parallelepiped. A prism with a parallelogram-shaped base, a hexahedron with three pairs of parallel faces, and a polyhedron with six faces, each of which is a parallelogram.
There are pairs of parallel and congruent faces. The parallelepiped has twelve (12) edges and eight (8) vertices. The edges of the parallelepiped can be split into three (3) sets of four (4) edges each, where the edges in each set are all parallel and the same length. The parallelepiped is also a zonohedron.
A parallelepiped is a three-dimensional object having six faces and a parallelogram-like design. It has 8 vertices, 6 faces, and 12 edges. The parallelepiped is also known by the names rhombic, cuboid, and cube.
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a cellist tunes the c-string of her instrument to a fundamental frequency of 65.4 hz. the vibrating portion of the string is 0.615 m long and has a mass of 14.8 g .
(A) With 268.94 N tension must she stretch it.
26% increase in tension is needed to increase the frequency from 65.4 Hz to 73.4 Hz, corresponding to a rise in pitch from C to D.
Part (A)
Fundamental frequency =f0= 65.4 Hz.
The length of the vibrating portion of the string = l = 0.615 m
Mass= m = 14.8 g
We know, [tex]f_0 = \frac{v}{2l}[/tex]
So, the value of v will be 65.4*2*0.615 = 80.442 m/s
As, We know,
[tex]T=\frac{v^2}{\frac{m}{l}}[/tex]
So, the value of tension will be: [tex]\frac{80.442^2}{\frac{14.8}{0.615}}=\frac{6470.91}{24.06}=268.94\:N[/tex]
Part (B)
Fundamental frequency =f0= 73.4 Hz.
The length of the vibrating portion of the string = l = 0.615 m
Mass= m = 14.8 g
We know, [tex]f_0 = \frac{v}{2l}[/tex]
So, the value of v will be 73.4*2*0.615 = 90.282 m/s
As, We know,
[tex]T=\frac{v^2}{\frac{m}{l}}[/tex]
So, the value of tension will be: [tex]\frac{90.282^2}{\frac{14.8}{0.615}}=\frac{8150.8395}{24.06}=338.77\:N[/tex]
So, the percentage increase in tension will be [tex]\frac{338.77-268.94}{268.94}\times 100\%=25.96\% \approx 26\%[/tex]
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The complete question should be:
a cellist tunes the c-string of her instrument to a fundamental frequency of 65.4 hz. the vibrating portion of the string is 0.615 m long and has a mass of 14.8 g .
Part A: With what tension must she stretch it?
Part B
What percent increase in tension is needed to increase the frequency from 65.4 Hz to 73.4 Hz, corresponding to a rise in pitch from C to D?
A gymnast uses a flexible stick to jump over the bar. Which of the following
describes energy changes when he reaches the highest point of his jump?
When the gymnast starts to jump his potential energy starts to convert to kinetic energy. But when he reaches the maximum height and stop there for seconds, potential energy regains. Thus, option C is correct.
What is potential energy?Potential energy of an object is the energy stored in it by virtue of its position. Potential energy increases with increases in mass and height which is clear from the equation for potential energy
p = mgh
Kinetic energy is generated by motion of the object. Thus, only a moving body attains a kinetic energy. Kinetic energy depends on the mass and velocity of the object.
Here, the gymnast gains a kinetic energy when he starts to jump from rest. But, when he reaches the maximum height where the speed slows down, his kinetic energy converts to potential energy. Thus, option C is correct.
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Your question is incomplete. But your complete question probably was:
A gymnast uses a flexible stick to jump over the bar. Which of the following
describes energy changes when he reaches the highest point of his jump?
A) kinetic- potential- potential
B) kinetic- potential- kinetic
C) potential - kinetic – potential
D) potential- potential- kinetic
Given that A + B = 0, (a) how does the magnitude of B compare with the magnitude of A? (b) How does the direction of B compare with the direction of A?
If A + B = 0, then the magnitude of B is equal to the magnitude of A. This is because the magnitude of a vector is simply its size or length, and if two vectors add up to zero, then their magnitudes must be equal.
As for the direction of B, it is the opposite of the direction of A. This is because if two vectors are equal in magnitude and opposite in direction, their sum will be zero. For example, if A is a vector pointing to the right and B is a vector pointing to the left, their sum will be zero. Similarly, if A is a vector pointing upwards and B is a vector pointing downwards, their sum will also be zero.
In summary, if A + B = 0, then the magnitude of B is equal to the magnitude of A, and the direction of B is opposite to the direction of A.
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Which statement best explains the purpose of making the loop of wire turn between the permanent magnets in an electric generator?
OA. The magnetic fields of the magnets cause electric charges in the
moving wire to flow.
B. The poles of the magnets reverse while the loop of wire is in
motion.
OC. The electric charges in the loop are repelled if the loop of wire
stops turning.
D. The electric current in the loop causes a magnetic field to form
around the moving wire.
Answer: C
Explanation:
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A student releases the 4kg bob of a 0.47m long
pendulum from the position shown.
What is the period of the harmonic motion?
S
What is the frequency of the harmonic motion?
Hz
How many cycles would the pendulum make in
45s?
6
(You may answer with a decimal)
6°
Projectile launch is a kinematics application to the movement of objects near the earth's surface.
How to find Projectile launch?Since the acceleration is constant, the time it takes for the body to go up is equal to the time it takes to go down; thus, the time it takes to go up is half of the total time.
tu = ttotal/2
tu = 4.70 / 2
tu = 2.35 s
The height the ball reach
The point of maximum height where the vertical velocity is zero
vy = voy - gt
0 = voy - gt
voy = gt
= 9.8 x 2.35
= 23 m / s
By using the equation.
v²y = v²oy - 2gy
0 = v²oy - 2gy
y = v²oy/2g
y = 23²/2 x 9.8
y = 27 m
To find the initial velocity,
Initial vertical velocity = 23 m / s
vx = x/t
The throw range is 44m in time of 4.60 s
vₓ = 44 / 4.60
v₀ = [tex]\sqrt{v^{2}ox + v^{2}oy }[/tex]
v₀ = [tex]\sqrt{9.56^{2}+23^{2} }[/tex]
v₀ = 24.9 m / s
The launch angle is:
Let's use trigonometry
tan θ = voy/vox
θ = tan⁻¹ voy/vox
θ = tan⁻¹ 23/9.56
θ = 67.4°
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A toy spacecraft is launched directly upward. When the toy reaches its highest point, a spring is released and the toy splits into two parts with masses of 0.01 kg and 0.09 kg, respectively. Immediately after the separation, the 0.01 kg part moves horizontally due east. Air resistance is negligible. True statements about the 0.09 kg part include which of the following? I. It could move north immediately after the spring is released. II. It takes longer to reach the ground than does the 0.01 kg part. III. It strikes the ground closer to the launch point than does the 0.01 kg part. (A) I only (B) III only (C) I and II only (D) II and III only (E) I, II, and III
Air resistance is hardly noticeable. true regarding the 0.09-kilogram component. This causes 0.01kg to land farther from the launch site than 0.09kg did.
0.09kg will move to the west due to momentum conservation (opposite of 0.01 kg). Additionally, since both are at the same height above the ground, it will take them equal amounts of time to descend to the ground.
Allowing v to be the speed of 0.01 kg, which means that the speed of 0.09kg will be smaller than 0.01 kg,
0.01v - (0.09)V = 0
V = 0.01 v/ 0.09 = 0.111v
The speed of 0.09 kg = 0.111v
The speed of 0.09 kg is less than 0.01kg.
Because of this, 0.01kg hits the ground farther from the launch point than 0.09kg did.
The amount of resistance in an electrical circuit represents the resistance to current flow. The Greek letter omega (), which represents resistance, represents ohms. German physicist Georg Simon Ohm (1784–1854), who investigated the connection between voltage, current, and resistance, is the name given to the unit of resistance known as an ohm.
Resistance measurements are typically performed in order to evaluate the health of a component or a circuit.
Current flow is inversely correlated with resistance. Conductor damage from corrosion or burning could be one of several potential causes if it is extremely high.
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five coins are stacked in the smooth plastic container. if each coin weighs 0.0235 lb, determine the normal reactions of the bottom coin on the container at points a and b.
The smooth plastic jar has five pennies placed inside of it. The normal reactions of the bottom coin on the container at locations a and b will be 0.0705 lb and 0.1175 lb respectively if each coin weighs 0.0235 lb.
What does normal force mean?A contact force, the normal force is often referred to as the normal reaction force. On two surfaces that are not attached to one another, a normal force cannot be applied.
What normal force is present during deceleration?The body's weight determines the usual deceleration force. A body's position relative to the ground tells us when it is about to fall. The normal force is the portion of a force that is perpendicular to any contact surface.
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A potato falling vertically downward is struck by a dart that is traveling vertically upward, as shown above. The dart and potato then collide, stick together, and continue moving after the collision.The weight of the dart is W. Which of the following claims best describes the magnitude of the net force on the dart immediately before, during, and immediately after the collision with the potato?
Option B is Correct
The velocity of the center of mass remains constant before the collision, when they collide there is a slight decrease in kinetic energy of the system since the collision is inelastic, resulting in a slight decrease of velocity, afterwards the velocity is constant again.
Velocity is the directional velocity of a moving object, observed from a given frame of reference and indicating the rate of change of position measured at a given time reference (eg 60 km/h northward). Velocity is a fundamental concept in kinematics, a branch of classical mechanics that describes the motion of bodies.
Velocity is a physical vector quantity. Both magnitude and direction are required to define it. The scalar absolute value (magnitude) of velocity is called velocity, and its magnitude is a consistent derived unit measured in the SI (metric) system as meters per second (m/s or m⋅s−1). For example, " meters/second" is a scalar, but "5 meters/second east" is a vector. An object is said to be accelerating if its velocity, direction, or both change.
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A converging lens with a focal length of 40 cm and a diverging lens with a focal length of -40 cm are 160 cm apart. A 2.5 cm-tall object is 60 cm in front of the converging lens.
Calculate the image position. cm in front of the second lens.
Calculate the image height.
1.25 cm is the height of the image. 160 cm separates a converging lens with such a 40 cm focal length from a diverging lens with the a -40 cm focal length. The converging lens is 60 cm away from a 2.5 cm tall item.
What does a converging or diverging lens mean?A lens that conforms a parallel source beam of light is known as a converging lens. One kind of converging lens is a double convex lens. Converging Lens A lens that separates a parallel light beam is known as a diverging lens. Diverging lenses include those that are double concave.
For the diverging lens, this image height corresponds to object height. We obtain h ′D=(20cm40cm)(5.0cm)=1.25cm again for diverging lens as a result.
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- A basketball strikes the rim of the basket. Explain each force in the force pair.
A basketball experiences four forces as it soars through the air. The ball is being pulled down to the Earth by gravity, being propelled upward by buoyancy, and slowed down due to the drag force created by the air it collides with.
What is force ?A force is an influence that has the power to alter an object's motion. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.
For instance, a basketball will strike the ground hard when it is dribbled. The ground's force on the ball is balanced by this force of the ball on the ground. The ball is sent upwards by the second force since it acts in the opposite direction. There are numerous characteristics of motion that depend on this interaction.
Thus, A basketball experiences four forces as it soars through the air.
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A taxi company is trying to decide whether to purchase brand A or brand B tires for its fleet of taxis. To estimate the difference in the two brands, an experiment is conducted using 12 of each brand. The tires are run until they wear out. The results are Brand A: \overline{x}_1 = 36. 300 x
1
=36.300 kilometers, s_1s 1
= 5000 kilometers. Brand B: \overline{x}_2 = 38. 100 x
2
=38.100 kilometers, s_2 = 6100s 2
=6100 kilometers. Compute a 95% confidence interval for \mu A − \mu BμA−μB assuming the populations to be approximately normally distributed. You may not assume that the variances are equal.
A 95% confidence interval for μA-μB is 0.025
If we want to make a 95% confidence interval estimate for an unknown population mean. This means that there is a 95% probability that the confidence interval will have the true population mean.
Thus, P( [sample mean] - margin of error < μ < [sample mean] + margin of error) = 0.95.
We have,
n1 = 12
s1 = 5000
mean x1 = 36300
n2= 12
s2 =6100
mean x2 =38100
We have to find 95%confidence interval for μA- μB
from 95% = 100 (1-α%)
1-α = 0.95
α = 1-0.95 =0.05
α/2 = 0.025
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