Answer:
b)3:2
Explanation:
The dispersive power is the reciprocal of the focal length:
[tex]P=\frac{1}{f}[/tex]
Given the ratio of focal lengths:
[tex]\frac{f_1}{f_2} = \frac{2}{3}\\\\\frac{\frac{1}{P_1}}{\frac{1}{P_2}}=\frac{2}{3}\\\\\frac{P_2}{P_1}=\frac{2}{3}\\\\\frac{P_1}{P_2}=\frac{3}{2}[/tex]
Therefore,
P₁ : P₂ = 3 : 2
Hence, the correct option is:
b)3:2
Naomi Osaka, a Japanese-African-American tennis player is the 2021 Australian Open Champion, and the first Asian tennis player in Women's Tennis Association (WTA) history to be ranked first in Singles. To celebrate her win, Naomi Osaka hits a ball into the stands at 40. m/s and at an angle 30.° above the horizontal. On its way down, the ball is caught by a spectator 12 m above the point where the ball was hit.
a) Calculate the time it takes the tennis ball to reach the spectator.
b) Calculate the ball's horizontal range (horizontal distance travelled).
Answer:
(a) t = 0.75 s
(b) d = 26 m
Explanation:
Height, h = 12 m
Angle, A = 30 degree
initial velocity, u = 40 m/s
(a) Let the time is t.
Use second equation of motion
[tex]h = u t + 0.5 at^2\\\\12 = 40 sin 30 t - 0.5 \times10 \times t^2\\\\12 = 20 t - 5 t^2\\\\5 t^2 - 20 t + 12 =0 \\\\t = \frac{20\pm \sqrt{400-240}}{10}\\\\t = \frac{20\pm 12.65}{10}\\\\t = 3.3 s, 0.75 s[/tex]
(b) d = u cos A t
d = 40 x cos 30 x 0.75 = 26 m
According to Coulomb’s Law, what happens to the force when the distance increase between 2 particles?
Answer:
The size of the force varies inversely as the square of the distance between the two charges. Therefore, if the distance between the two charges is doubled, the attraction or repulsion becomes weaker, decreasing to one-fourth of the original value.
Explanation:
Coulomb’s law, mathematical description of the electric force between charged objects. Formulated by the 18th-century French physicist Charles-Augustin de Coulomb, it is analogous to Isaac Newton’s law of gravity.
Both gravitational and electric forces decrease with the square of the distance between the objects, and both forces act along a line between them. In Coulomb’s law, however, the magnitude and sign of the electric force are determined by the electric charge, rather than the mass, of an object. Thus, charge determines how electromagnetism influences the motion of charged objects. Charge is a basic property of matter. Every constituent of matter has an electric charge with a value that can be positive, negative, or zero.
Coulomb's Law says that the force between 2 charges is proportional to the product of the quantities of charge on each and inversely proportional to the square of the distance between them. The formula for Coulomb's Law is [tex]F=k\frac{q_{1}q_{2} }{r^{2} }[/tex].
[tex]F[/tex] is the force.
[tex]k[/tex] is the Coulomb's constant ([tex]8.987*10^{9} \frac{Nm^{2} }{C^{2} }[/tex]).
[tex]q_{1}[/tex] is the electric charge of object 1.
[tex]q_{2}[/tex] is the electric charge of object 2.
[tex]r[/tex] is the distance between the two charges.
Electric force is inversely proportional to ([tex]r^{2}[/tex]) instead of ([tex]r[/tex]). As the distance between charges increases, the electric force decreases by a factor of [tex]\frac{1}{r^{2} }[/tex].
can anyone help me with this?
the question : find the value of the resistors
Answer:
Value of the resistors R = 2 ohm
Explanation:
Given:
Resistor R1 = 4 ohm
Resistor R2 = 4 ohm
Find:
Value of the resistors R
Computation:
We know that Resistor R1 and Resistor R2 connected in parallel series.
So,
Using common resistance in parallel series
⇒ 1/R = 1/R1 + 1/R2
⇒ 1/R = 1/4 + 1/4
⇒ 1/R = (1 + 1) / 4
⇒ 1/R = 2/4
⇒ R = 4/2
⇒ R = 2
Value of the resistors R = 2 ohm
If a planet has the same mass as the earth, but has twice the radius, how does the surface gravity, g, compare to g on the surface of the earth
Answer:
The surface gravity g of the planet is 1/4 of the surface gravity on earth.
Explanation:
Surface gravity is given by the following formula:
[tex]g=G\frac{m}{r^{2}}[/tex]
So the gravity of both the earth and the planet is written in terms of their own radius, so we get:
[tex]g_{E}=G\frac{m}{r_{E}^{2}}[/tex]
[tex]g_{P}=G\frac{m}{r_{P}^{2}}[/tex]
The problem tells us the radius of the planet is twice that of the radius on earth, so:
[tex]r_{P}=2r_{E}[/tex]
If we substituted that into the gravity of the planet equation we would end up with the following formula:
[tex]g_{P}=G\frac{m}{(2r_{E})^{2}}[/tex]
Which yields:
[tex]g_{P}=G\frac{m}{4r_{E}^{2}}[/tex]
So we can now compare the two gravities:
[tex]\frac{g_{P}}{g_{E}}=\frac{G\frac{m}{4r_{E}^{2}}}{G\frac{m}{r_{E}^{2}}}[/tex]
When simplifying the ratio we end up with:
[tex]\frac{g_{P}}{g_{E}}=\frac{1}{4}[/tex]
So the gravity acceleration on the surface of the planet is 1/4 of that on the surface of Earth.
Define Newton's law of motion?
define regular body in science
Answer:
All the sides and inner angles of a regular form must be equal. The sides and angles of an irregular form aren't the same. An equilateral triangle, for example, is a regular form because all of its sides and angles are the same length.
OAmalOHopeO
When extrication will involve cutting the roof off a vehicle, stabilization of the vehicle should include:
Answer:
Deflating the tires by pulling the valve stems
Explanation:
When an accident happens, the EMT process is to take off the top of the vehicle of the highly damaged vehicle so that it can easily be assessed to rescue the vehicle occupants. This creates a bigger exit for the rescuers to take out the people. Vehicle extrication means removing the vehicle from around someone involved in a fatal collision, when other other ways of exiting is not advised or possible. to stabilize the vehicle you have to deflate all tires by pulling the valve stems.
Explain how two rolling bowling balls of different masses can have the same momentum
Knowing that the momentum(p) of an object is directly (when one number goes up the other will too) related to both the mass and velocity of an object or p=mv, two rolling bowling balls of different masses can have the same momentum because the one with the lower mass, has a higher velocity. The higher velocity of an object would make up for the lower mass and vice versa.
Answer:
Sample Response: Momentum is equal to the mass of an object multiplied by the velocity of an object. The two bowling balls can have the same momentum if the bowling ball with less mass has a higher velocity, and vice versa. As long as the product of the mass and velocity of one bowling ball is equal to the product of the mass and velocity of the other, the bowling balls will have the same momentum.
Explanation:
A system of releases 125kJ of heat while 104kJ of work is done in the system. Calcilate the change om imternal energy (in kJ)
Answer:
DU = 21 KJ
Explanation:
Given the following data;
Quantity of heat = 125 KJ
Work = 104 KJ
To find the change in internal energy;
Mathematically, the change in internal energy of a system is given by the formula;
DU = Q - W
Where;
DU is the change in internal energy.
Q is the quantity of energy.
W is the work done.
Substituting into the formula, we have;
DU = 125 - 104
DU = 21 KJ
100 g of water are cooled and the enthalpy change is -12,540 J. What is the change in temperature of the water?
Answer:
-29.9907
Explanation:
c = Q / (mΔT)
You're looking for ΔT, so you would plug in what you already know and get C= -12540/(100 x ΔT)
then you would solve
Which type of stress is most likely the cause of irritability?
eustress
O hypostress
O distress
O peripheral stress
Answer:
The correct answer is - distress.
Explanation:
Eustress is a type of stress that is beneficial to person and caused by adrenaline. Hypostress is a stress that is caused due to boredom or no work. It is stress comes with wasting the time.
Distress is the bad stress caused by anxiety, sadness, grief, and such type of stress that is caused irritability. Irritability is caused not just by stress but many factors.
what is energy
and how it works?
Answer:
Energy is defined as the ability to do work.
Explanation:
Energy is a property that must be transferred to a body to perform work on the body. Energy can be found in many things and can take different forms.Energy is never lost, but it can be converted from one form to another.Fossil fuels are the largest sources of energy for energy generation.TRUE OR FALSE. if an object covers equal distance at equal intervals of time, then it is moving at constant speed and not accelerating
Answer:
True
Explanation:
Speed = distance/time
If distance and time are the same, then the right hand side of the equation remains the same, causing us to solve the left to the same value
As the distance is the same (say 50m) and the time is the same (say 50s) then the speed must be the same (1m/s)
In a softball game a batter hits at the velocity of 28 and an angle shown 45 below . What is the maximum range of the ball
Answer:
80 m
Explanation:
Given :
Initial Velocity, U = 28 m/s
θ = 45°
The maximum range occurs at angle, θ = 45°
The maximum range, R is given by ;
R = U²sin2θ / g
g = acceleration due to gravity = 9.8 m/s²
Plugging in the values :
R = [28² * sin2(45)] / 9.8
R = [28² * sin90] / 9.8
R = 784 / 9.8
R = 80 m
Internal energy of a diatomic gas consists of:
OA. kinetic energy due to vibration and rotation.
B. kinetic energy due to translation, vibration, and rotation.
C. potential energy due to intermolecular forces.
D. kinetic energy due to translation only.
Answer:
C) Potential energy due to intermolecular forces.
Look at the distance-time graph below. It shows Angela's journey as she walks to the end of the road and back. The end of the road is 40 m away. After how many seconds did she arrive back where she started?
Answer:
Explanation:
If the distance to the end of the road was 40 m, and she traveled back to where she started, she traveled a total distance of 80 m. It took her 100 seconds to travel the 80 m.
Based on the given distance-time graph, the number of seconds that Angela used to go to the end of the road and arrive back is 100 seconds.
How long did Angela take?The end of the road is 40m and coming back is also 40 m. The total distance is:
= 40 + 40
= 80m
The graph shows that to walk 80 meters, Angela took a 100 seconds because the line on the graph ends at 80 m and 100 seconds.
Find out more uses of distance-time graphs at https://brainly.com/question/13877898.
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It takes 130 j of work to compress a certain spring 0.10m. (a) what is the force constant of this spring? To compress the spring an additional 0.10m, does it take 130
Answer:
Explanation:
The PE equation for a mass/spring system is
[tex]PE=\frac{1}{2}k[/tex]Δx² and filling in:
[tex]130=\frac{1}{2}k(.10)^2[/tex] and
[tex]k=\frac{2(130)}{(.10)^2}[/tex] so
k = 26000 N/m
If the displacement from equilibrium changes more, the PE needed to compress it will also change.
[tex]PE=\frac{1}{2}(26000)(.20)^2[/tex] gives us that
PE = 520J
1. A rocket is forced forward by the ______ force of its engines, expelling gases out the rear of the rocket.
There are two forces acting on a rocket at the moment of lift off: Thrust pushes the rocket upwards by pushing gases downwards in the opposite direction.Weight is the force due to gravity pulling the rocket downwards towards the centre of the earth.So I'm thinking the answer is THRUST.
why is oil denser than air
Answer:
The molecules of oil are more packed together than those of air.
The Earth orbits around the sun because the gravitational force that the sun
exerts on the Earth:
O A. causes Earth's acceleration toward the sun.
O B. is very small because the sun is so far from the Earth.
O c. is smaller than the force the Earth exerts on the sun.
O D. pushes the Earth away from the sun.
The Earth orbits around the sun because the gravitational force that the sun
exerts on the Earth:
O A. causes Earth's acceleration toward the sun.
O B. is very small because the sun is so far from the Earth.
O c. is smaller than the force the Earth exerts on the sun.
O D. pushes the Earth away from the sun.
Answer -:O A. causes Earth's acceleration toward the sun.
I hope this helps, have a nice time ahead!
a tennis ball “A” is released from rest down a 10.0 m long inclined ramp with a uniform acceleration of 5.0 m/s2. Another tennis ball “B” is initially located at the same height as ball “A” right above the lower edge of the ramp. Ball “B” is thrown upward with some initial speed at the same instant as the release of ball “A”.
a) What was the initial velocity of ball "B" so that "A" and "B" reach the bottom of the ramp at the same time?
Answer:
Please find the complete question in the attached file.
Explanation:
The time is taken by ball A to reach the bottom [tex]\to t=\sqrt{\frac{2s}{a}}=\sqrt{\frac{2 \times 10}{5}}=\sqrt{\frac{2 0}{5}}= \sqrt{4}=2\ s[/tex]
Calculating the velocity of the ball:
[tex]-h=ut-\frac{1}{2}gt^2\\\\-S \sin 30=ut-\frac{1}{2}gt^2\\\\-5=u(2)-\frac{1}{2}\times 9.81 \times 2^2\\\\[/tex]
[tex]-5=2u-9.81 \times 2\\\\-5=2u-19.62\\\\-5+19.62=2u\\\\14.62=2u\\\\u=\frac{14.62}{2}\\\\u=7.31 \ \frac{m}{s}[/tex]
How can one form of energy be transferred into another.
Energy can be transferred mechanically through the movement of the parts in machines, and when the motion or position of an object changes. Sound waves and seismic waves (formed during earthquakes) are mechanical waves that transfer energy through materials and from place to place.
Hope This Helps :)
Does the colour of an object affect the rate of evaporation?
A body weighs 63 N on the surface of the earth. What is the gravitational force on it due to the earth at a height of 3200 km from the earth's surface? (Radius of the earth is 6400 km)
Answer:
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how to Calculate the pressure on its base.
Answer:
p is =force x 10 whch is constant
A boat takes off from the dock at 2.5m/s and speeds up at 4.2m/s2 for 6.0 seconds how far has the boat traveled
Answer:
The answer is "91 m"
Explanation:
[tex]v_0 = 2.5 \ \frac{m}{s}\\\\a = 4.2\ \frac{m}{s^2}\\\\t = 6.0\ s\\\\\Delta x=?[/tex]
Using formula:
[tex]\Delta x = v_0 t +\frac{1}{2} at^2\\\\[/tex]
[tex]= 2.5 \times 6.0 +\frac{1}{2} \times 4.2 \times 6.0^2\\\\= 90.6\ m \approx 91\ m[/tex]
Jake launches a water balloon at an angle of 35° above the horizontal. If he sends it flying with an initial velocity of 3 m/s, how far away does Fred (who is the same height as Jake) need to be for it to hit him (assuming Jake has a good aim)?
Answer:
R = 0.86 m
Explanation:
The formula for the range of the projectile motion can be used here:
[tex]R = \frac{v^2 Sin2\theta}{g}[/tex]
where,
R = Range of projectile = distance between Jake and Fred = ?
v = launch speed = 3 m/s
θ = Launch Angle = 35°
g = acceleration due to gravity = 9.81 m/s²
Therefore,
[tex]R = \frac{(3\ m/s)^2Sin[(2)(35^o)]}{9.81\ m/s^2}\\\\[/tex]
R = 0.86 m
Which statement is correct about how the temperature of an object changes?
Group of answer choices
The molecules making up object collide with the molecules of the other and some of the potential energy from a cooler object is transferred to the warmer one.
The molecules making up object collide with the molecules of the other and some of the kinetic energy from a warmer object is transferred to the cooler one.
The molecules making up object collide with the molecules of the other and some of the kinetic energy from a cooler object is transferred to the warmer one.
The molecules making up object collide with the molecules of the other and some of the potential energy from a warmer object is transferred to the cooler one.
The molecules making up object collide with the molecules of the other and some of the kinetic energy from a warmer object is transferred to the cooler one.
Having the correct posture and the degree or severity of braking, acceleration and steering inputs have a direct result on the ability of a motorist to effectively address changes in __________?
Answer: Vehicle Balance
Explanation:
Vehicle balance simply means how the weight of a vehicle is distributed across its tires which connects to the road
It should be noted that there'll be a shift in the balance of a vehicle when the braking, acceleration, or turning bring about a scenario in which the weight of th vehicle moves from one area to another.
What is meant by measurement? l
Answer:
The action of measuring the size, length, or amount of something, as established is called measurement.
Explanation:
“Measurement” is the act of determining a target's size, length, weight, capacity, or other aspect. ... To use measurement tools as necessary. It is also appropriate to say that measurement is done by a worker using a measurement system, and instrumentation is done by a technician.
