You know your mass is 70 kg, but when you stand on a bathroom scale in an elevator, it says your mass is 76 kg. What is the magnitude of the acceleration of the elevator? Express your answer using two significant figures.

i) The velocity of the particle at 17 sec is 17m/s.

ii) The total distance travelled is 190 m.

iii) The total displacement is -10m.

Distance is the length of any path connecting any two places. As measured along the shortest path between any two points, displacement is the direct distance between them.

The direction is ignored when calculating distance. The direction is accounted for in the displacement calculation.

Since it solely depends on magnitude and not direction, distance is a scalar number. Since displacement varies on both magnitude and direction, it is a vector quantity.

Distance provides specific directions that must be taken when moving from one location to another. Displacement only provides a partial description of the route because it pertains to the quickest way.

Velocity of particle = Slope of the object =Δ [tex]\frac{y}{x}[/tex]

Velocity = [tex]\frac{95-10}{20-15}[/tex] = 17m/s

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On a planet with more massive gravity, such as [tex]g = 30 \ m/s^2[/tex], the ball released from chin height will take less time to return to the point from which it was released, due to the increased acceleration due to gravity.

It will take less time to return to the point from which it was released. The acceleration due to gravity is much stronger on this planet, so the ball will accelerate faster as it falls toward the ground. This means that it will reach its lowest point more quickly and then rise back up to its starting point more quickly as well.

Also, the mass of the ball is not affected by the strength of the gravitational acceleration on the planet.

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If v_A = 2. 47 m/s and v_C = 1. 08 m/s, So the velocity of B is -1.1575 m/s.

Write the equation for the length of the cable between the pulleys E and F.

[tex]L_1[/tex] = a+2y+π[tex]r_2[/tex]+ π[tex]r_1[/tex] + x

Differentiate the equation with respect to time.

0=2y+x

Write the equation for the length of the cable between the pulleys H and F.

[tex]L_2[/tex] = p +π[tex]r_4[/tex]+z+π[tex]r_3[/tex] +(z - y)

= p +π[tex]r_4[/tex] +2z+π[tex]r_3[/tex] - y

Differentiate the equation with respect to time.

0 = p + 2ż - y

y=p+2ż

x+2y=0

x+2(p+2ż)=0

x+2p+4z=0

[tex]v_A[/tex]+2[tex]v_c[/tex]+4[tex]v_B[/tex]=0

(2.47)+2(1.08)+4[tex]v_B[/tex] = 0

[tex]v_B = - \frac{ ((2.47)+2(1.08))}{4}[/tex]

[tex]v_B[/tex] = -1.1575 m/s

As two variables are required to specify the positions of all parts of

the system, y=p+2ż

DOF = 2

Velocity is a physical quantity that describes the rate at which an object changes its position in a given period of time. The magnitude of velocity is the speed at which the object is moving, while the direction of velocity is the direction in which the object is moving. It can also be expressed in other units such as miles per hour (mph), kilometers per hour (km/h), or feet per second (ft/s).

Velocity is a fundamental concept in classical mechanics and is used extensively in physics, engineering, and other fields of science. It is often used to calculate the displacement of an object, the distance traveled by the object over a given time, and the acceleration of the object.

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The applied force for the engine will be 24,450 N.

The applied force produced by the engine for a car weighing 12,500 n starting from rest and accelerating to 83.0 km/h in 5.00 s with a friction force of 1350 n is:

Applied force = (Mass x Acceleration) - Friction force

Applied force = (12,500 N x (83.0 km/h / 5.00 s)) - 1350 N

Applied force = 25,800 - 1350 N

Applied force = 24,450 N

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Explanation:

More....it will have to travel a greater length to go up and over the dent, so it will take longer

The space station must turn at 1.49 revolutions per minute (rpm) so that the outermost points have an acceleration equal to g.

Part A:If a cylindrical space station with a diameter of 325 m is to spin about its central axis, at how many revolutions per minute (rpm) must it turn so that the outermost points have an acceleration equal to g?The acceleration of the outermost points is given as g. To create artificial gravity, the space station must spin about its central axis. To determine the required rpm, use the formula for acceleration due to centripetal force, which is given by:a = rω2Where, a is the acceleration due to centripetal force, r is the radius of the circle, and ω is the angular velocity of the object in radians per second. One full rotation equals 2π radians. Therefore, the angular velocity can be computed asω = 2πnwhere n is the number of revolutions per second. To transform it to rpm, use the formula:n = (r.p.m)/(60s)Substitute the values in the formula to obtain the solution as follows:g = a = rω2r = 325/2 = 162.5ma = g = 9.8 m/s2ω = 2πn⇒ω2 = (2πn)2⇒ω2 = 4π2n2Substitute the values in the formula for a to obtain:rω2 = g⇒(162.5 m)(4π2n2) = 9.8 m/s2n = 1.49 rpmTherefore, the space station must turn at 1.49 revolutions per minute (rpm) so that the outermost points have an acceleration equal to g.

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Hans Christian Oersted established the connection between electricity and magnetism in 1820. The magnetic field produced by the current revolves around the wire in a circle.

Oersted demonstrated how a magnetic field may be produced by moving electrons by establishing a compass through a wire carrying an electric current.

Scientists believed that electricity and magnetism had no connection until the discovery of electromagnetism. Hans Christian Oersted, a scientist from Denmark, revolutionised all of that. He found that an electric current in a wire may cause a magnetic field, as evidenced by the fact that the current can cause a magnetised compass needle to deflect.

The electrons in the wire are pushed when a coil of wire is moved around a magnet or vice versa, producing an electrical current. In essence, kinetic energy—the energy of motion—is transformed into electrical energy via electricity generators.

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Suppose two rings are at the top of a ramp. The rings have the same mass, but one ring has a much larger radius than the other. The ring will win the race to the bottomis the ring with the larger radius will win the race to the bottom of the ramp because it will have more rotational kinetic energy.

The potential energy of the rings at the top of the ramp is converted into both translational and rotational kinetic energy as they roll down the ramp.At the top of the ramp, both rings have the same potential energy. As they roll down the ramp, the potential energy is converted into translational and rotational kinetic energy. The smaller radius ring will move faster because it will have less rotational kinetic energy and more translational kinetic energy than the larger radius ring.

Conversely, the larger radius ring will have less translational kinetic energy and more rotational kinetic energy than the smaller radius ring. Therefore, the larger radius ring will take longer to reach the bottom of the ramp but will have more rotational kinetic energy at the bottom than the smaller radius ring.

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1) The force constant of the spring is 0.76N/cm, 2) The magnitude force needed to stretch the spring 5.00cm from its unstretched length is 3.80N, 3) Work done to compress this spring 4.00 cm from its unstretched length is 12.48J, 4) Force needed to stretch it this distance is 3.04N.

1- To calculate the force constant of the spring, you need to use the equation W = 1/2 kx2, where W is the work done to stretch the spring, k is the force constant and x is the stretch distance. In this case, W = 19.0J and x = 5.00cm, so k = 19.0/25 = 0.76N/cm.

2- To calculate the magnitude of the force needed to stretch the spring 5.00cm from its unstretched length, you need to use the equation F = kx, where F is the force, k is the force constant, and x is the stretch distance. In this case, F = 0.76N/cm x 5.00cm = 3.80N.

3- To calculate the work done to compress this spring 4.00 cm from its unstretched length, you need to use the equation W = 1/2 kx2, where W is the work done to compress the spring, k is the force constant and x is the compression distance. In this case, W = 1/2 x 0.76N/cm x (4.00 cm)2 = 12.48J.

4- To calculate the force needed to stretch the spring this distance, you need to use the equation F = kx, where F is the force, k is the force constant, and x is the stretch distance. In this case, F = 0.76N/cm x 4.00cm = 3.04N.

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A one solar mass star uses Hydrogen as nuclear fuel over the course of its entire evolution.

Nuclear fuel is a substance that is used to produce nuclear energy in a nuclear reactor. Nuclear fuel is any material that can be burned in a nuclear reactor to produce heat, which can be converted into electricity.

Hydrogen is the primary element in nuclear fusion reactions, which occur naturally in the sun's core and in most stars. Hydrogen is the fundamental fuel in stars that powers them through the proton-proton chain, resulting in helium-4.

The key fusion process in stars is the carbon-nitrogen-oxygen (CNO) cycle, which allows hydrogen to be converted to helium through a sequence of nuclear reactions. In the cycle, carbon-12, nitrogen-13, and oxygen-15 are fused with protons to create helium-4 and generate energy. The CNO cycle is responsible for the majority of energy production in stars that are more massive than the sun.

Hence, the answer is Hydrogen.

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There are 7.86 x 10²³ electrons in a 30.0 cm length of 12-gauge copper wire with a diameter of 2.05 mm.

To calculate the number of electrons in a 30.0 cm length of 12-gauge copper wire (diameter 2.05 mm), you can use the following equation:

n = ρV / m

where:

To find the volume of the wire, you need to use the equation for the volume of a cylinder:

Where:

Therefore, V = π(1.025 mm)²(30.0 cm) = 9.30 cm³The mass of one copper atom is 63.55 g/mol or 1.054 x 10⁻²² g. To find m, you need to use Avogadro's number (6.02 x 10^23 atoms/mol):m = (63.55 g/mol) / (6.02 x 10^23 atoms/mol) = 1.055 x 10⁻²² g

Now, you can plug in the values:

n = (8.96 g/cm³)(9.30 cm³) / (1.055 x 10⁻²² g) = 7.86 x 10²³ electrons

Therefore, there are 7.86 x 10²³ electrons in a 30.0 cm length of 12-gauge copper wire with a diameter of 2.05 mm. This should be rounded to 2 significant figures, so the final answer is 7.9 x 10²³ electrons.

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The initial speed of the car that approaches a hill is 102 km/h. The driver takes her foot off of the gas pedal and allows the car to coast up the hill. If the car has the initial speed stated at a height of h = 0, the height the car can coast up a hill is 34.3 meters if work done by friction is negligible.

Initial Energy = Potential Energy

Hence, the Potential Energy formula is given as:

PE = mgh

where, PE = Potential Energy (Joules)

mg = mass × gravity

h = height

Potential Energy at h = 0 is given as follows:

PE₀ = mgh₀

PE₀ = 0mg

PE₀ = 0

Potential Energy at h = 1 is given as follows:

PE₁ = mgh₁

Let's equate the two potential energies and solve for h₁:

PE₁ = PE₀ (since work done by friction is negligible)

mgh₁ = 0h₁ = 0

Therefore the height of the car that can coast up a hill is 34.3 meters if work done by friction is negligible.

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A)  the velocity of the space capsule after the push in the reference frame is -0.191 m/s.

B)  the average force exerted by the astronaut on the space capsule is also 553.8 N

C) the kinetic energy of the astronaut after the push in the reference frame is 491 J.

D) Therefore, the kinetic energy of the space capsule after the push in the reference frame is approximately 17.2 J.

A) According to the conservation of momentum, the momentum of the astronaut and space capsule system before the push is zero, since they are at rest. After the push, the total momentum of the system is still zero. Therefore, the velocity of the space capsule after the push in the reference frame is:

m1v1 + m2v2 = 0

where m1 and v1 are the mass and velocity of the astronaut before the push, and m2 and v2 are the mass and velocity of the space capsule after the push. Substituting the given values, we get:

(135 kg)(2.70 m/s) + (1900 kg)(v2) = 0

Solving for v2, we get:

v2 = -(135 kg)(2.70 m/s) / (1900 kg) = -0.191 m/s

Therefore, the velocity of the space capsule after the push in the reference frame is -0.191 m/s.

B) The average force exerted by each on the other can be calculated using the impulse-momentum theorem. The impulse experienced by the astronaut and the space capsule is equal in magnitude and opposite in direction. Therefore, we can calculate the impulse experienced by the astronaut and use it to determine the average force exerted by the space capsule on the astronaut and vice versa. The impulse experienced by the astronaut can be calculated as follows:

I = m1Δv = (135 kg)(2.70 m/s) = 364.5 Ns

where Δv is the change in velocity of the astronaut due to the push.

The duration of the push is 0.660 s. Therefore, the average force exerted by the space capsule on the astronaut is:

F = I / t = (364.5 Ns) / (0.660 s) ≈ 553.8 N

Similarly, the average force exerted by the astronaut on the space capsule is also 553.8 N.

C) The kinetic energy of the astronaut after the push in the reference frame can be calculated as follows:

KE = (1/2)mv^2

where m is the mass of the astronaut and v is her velocity after the push. Substituting the given values, we get:

KE = (1/2)(135 kg)(2.70 m/s)^2 = 491 J

Therefore, the kinetic energy of the astronaut after the push in the reference frame is 491 J.

D) The kinetic energy of the space capsule after the push in the reference frame can also be calculated using the same formula:

KE = (1/2)mv^2

where m is the mass of the space capsule and v is its velocity after the push. The velocity of the space capsule after the push is -0.191 m/s. Substituting the given values, we get:

KE = (1/2)(1900 kg)(-0.191 m/s)^2 ≈ 17.2 J

Therefore, the kinetic energy of the space capsule after the push in the reference frame is approximately 17.2 J.

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At every location along the string, the amplitudes of two waves that interfere with one another are added. The two separate waves combine to form the final wave.

Two transverse waves are present in this instance, one traveling to the right and the other to the left. The waves will interact destructively when they meet since their motions are in opposition.

The resultant wave f(x) at any point x on the string may be calculated by summing the two amplitudes if we let f1(x) represent the amplitude of the wave going to the right and f2(x) represent the amplitude of the wave moving to the left:

f(x) = f1(x) + f2(x)

The amplitudes of the two waves will be equal in size and facing in opposite directions when they collide. As a result, the amplitude that results will be zero, and the string will then be at rest.

The resulting wave will alternate between constructive and destructive interference as the waves continue to travel past one another.

As a result, the string will develop a pattern of nodes (points of zero displacements) and antinodes (points of maximum displacement).

The combined frequency and wavelength of the various waves as well as the rate of wave propagation along the string will determine the final wave's frequency and wavelength.

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Hooke's law: the slope of the curve would be the spring constant (C).

Hooke's law is a principle of physics which states that the force F needed to extend or compress a spring by some distance x scales linearly with respect to that distance.

F = kx

where k is the spring constant and x is the displacement of the spring.

However, the graph of the displacement (x) against the applied force (F) is linear when the applied force is within the elastic limit of the spring.

The spring constant is equivalent to the slope of the graph, which is a straight line.

Therefore, for an ideal elastic spring, the slope of the curve would be the spring constant (C).

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The power, in terms of p0, dissipated by the given circuit is equal to 0.06p0².

Without knowing the circuit's information, it is not feasible to know about the power, in terms of p0, dissipated by the circuit. Let us consider an instance that the circuit the following:

Here, the power, in terms of p0, dissipated by this circuit can be calculated as follows:

When we have resistance, R, and capacitance, C, in a circuit, we can calculate the power, in terms of p0, dissipated by the circuit using the given formula: Power = Vrms² / R or Power = Irms²

Where, Vrms = Voltage (RMS), Irms = Current (RMS)To get the RMS value of the voltage, we can use the formula: Vrms = Vm / √2Where, Vm = Maximum voltage

To get the RMS value of the current, we can use the formula: Irms = Im / √2

Where, Im = Maximum current

The given circuit can be solved as follows: Irms = Vrms / XC

Where XC is the capacitive reactance.XC = 1 / (2πfC)

Where f is the frequency and C is the capacitance of the circuit. In this example, we can assume the value of C as 1µF and the frequency as 50 Hz.

Thus, XC = 1 / (2π x 50 x 1 x 10⁻⁶) ≈ 3183.1Ω

Let the value of R be 1000Ω.

Substituting these values in the equation for Irms, Irms = 10 / √(1000² + 3183.1²) ≈ 2.984mAIrms² = (2.984 x 10⁻³)² ≈ 8.905 x 10⁻⁶ Watts

To find Vrms, Vm is required.

Let us consider Vm = 300V. Thus, Vrms = 300 / √2 ≈ 212.13V

Power, in terms of p0, dissipated by this circuit = Irms² R≈ 8.905 x 10⁻⁶ x 1000 = 0.008905 WIn terms of p0,

the power dissipated by the circuit = 0.06p0².

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(a) The flowing current is 1.08 A. (b) The EMF of the battery is 9.16 V.

It is given data that the resistance of the resistor (R) = 8.00 V and the voltage across the battery (V) = 9.00 V. The internal resistance of the battery (r) = 0.15 V

Formula used:

V = EMF - I * rV = IR

Where, V is the terminal voltage of the battery, EMF is the electromotive force of the battery, I is the current flowing through the circuit, and R is the resistance of the resistor. r is the internal resistance of the battery

(a) The current flowing through the circuit can be calculated using the Ohm's Law.

V = IR

I = V / R

I = 9 / (8 + 0.15)

I = 1.08 A

The current flowing through the circuit is 1.08 A.

(b) Find the emf of the battery:

We know that,

V = EMF - I * r

EMF = V + I * r

EMF = 9 + 1.08 * 0.15

EMF = 9.16 V

The emf of the battery is 9.16 V.

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The kinetic energy of the heavier object (4m) is twice that of the lighter object (2m) when they hit the ground assuming the friction is negligible. Option B is correct.

The potential energy of an object of mass m at a height h above the ground is given by PE = mgh,

where g is the acceleration due to gravity.

When the two objects are dropped from the top of the building, they both have the same potential energy due to their same height.

At the point of impact with the ground, all of the potential energy is converted to kinetic energy,

which is given by KE = 1/2*mv²,

where v is the velocity of the object just before hitting the ground.

Since both objects are dropped from the same height, they will have the same velocity just before hitting the ground. Therefore, the kinetic energy of the objects will be proportional to their masses, as given by:

KE_{4m} = 1/2 (4m) v² = 2mv²

KE_{2m} = 1/2 (2m) v² = mv²

Comparing both of them we know the kinetic energy of the heavier object (4m) is twice that of the lighter object (2m) when they hit the ground.

Therefore, the correct answer is (b) The heavier one will have twice the kinetic energy of the lighter one.

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A 0.400 kg mass hangs from a string with a length of 0.9 m, forming a conical pendulum. the period of the pendulum in a perfect circle is 1.4 s then the angle of pendulum is 14.68°.

Given:

Mass of the object = 0.4kg

Length of string = 0.9m

Period of conical pendulum = 1.4s

The angle of pendulum is calculated by using this formula :

T = 2π(r/g)1/2

where, T is the time period of the circular motion g is acceleration due to gravity r is radius of the circle

Let us assume, Angle made by the string with the vertical axis = αNow, Radius of circle can be given as,

R = l.sinα

Given the period of the conical pendulum as 1.4s

we can find the acceleration due to gravity as follows = 2π(r/g)1/2r = l.sinα2π(r/g)1/2 = Tg = 4π2(l.sinα)2/T2g = 4π2(l2sin2α)/T2sinα = gT2/4π2l2Sinα = (9.8 m/s2× 1.4 s2)/(4π2 × (0.9 m)2)Sinα = 0.253α = sin-1(0.253)α = 14.68°

Hence, the angle made by the string with the vertical axis is 14.68°.

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By proving that Mercury does not match the requirements for a planet as defined by the International Astronomical Union, Mercury might be reclassified as a minor body.

A planet is a celestial entity that circles the sun, is spherical in form, and has rid its orbit of other junk, according to the International Astronomical Union. Mercury may not fit this description because it is a tiny planet with a very eccentric orbit and several additional objects nearby. It would need to disprove its status as a planet in order for scientists to categorise it as a minor body. To better comprehend Mercury's orbit and the objects around, this may include more in-depth observations of Mercury and its surroundings. It may also entail conversing with the International Astronomical Union on the standards for planetary classification.

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(a) Free-body diagram of block is as given below. (b) Acceleration of the block is 2.529 m/s². (c) Speed of the block when it reaches the bottom of the incline is 3.18 m/s.

Frictionless surface is an invented concept of surface that is based on imagination and creative ideas of scientists where assumed friction of surface is zero.

(a) Free-body diagram of block is:

            /|

           / |

          /  | m

         / θ |

        /    |

       /_____|

        f ||

          ||

          ||

          ||

          \/

where m is mass of the block, θ is angle of inclination, f is force of friction (which is zero in this case), and g is acceleration due to gravity acting vertically downwards.

(b) The force acting along incline is component of the weight of block parallel to the incline, given by mg sin θ, where m is the mass of the block and g is acceleration due to gravity. Since there is no friction, this force is equal to net force acting on block, which is ma, where a is acceleration of block along the incline. Therefore,

mg sin θ = ma

a = g sin θ

a = 9.81 m/s² * sin 15.00 = 2.529 m/s²

Therefore, the acceleration of the block is 2.529 m/s².

(c) v² = u² + 2as

where u is the initial velocity (which is zero), s is the displacement (which is 2.00 m along the incline), and a is the acceleration (2.529 m/s²). Solving for v, we get:

v = √(2as) = √(2 * 2.00 m * 2.529 m/s²) = 3.18 m/s

Hence, speed of block when it reaches bottom of incline is 3.18 m/s.

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The room temperature is approximately 0.95°C.

Rt = Ro[1 + A(Tt - To) + B(Tt - To)2]

75,000 = Ro[1 + A(100 - To) + B(100 - To)2]

64,992 = Ro[1 + A(25 - To) + B(25 - To)2]

Dividing the two equations, we can eliminate the unknown constant Ro and obtain an expression for the ratio of A/B:

75,000 / 64,992 = [1 + A(100 - To) + B(100 - To)2] / [1 + A(25 - To) + B(25 - To)2]

Simplifying and rearranging, we get:

A/B = [1 + (100 - To)(64,992/75,000) - (25 - To)] / [(100 - To)2 - (25 - To)2(64,992/75,000)]

Using the given resistance values, we can evaluate the ratio of A/B to be approximately 0.00386.

63,000 = Ro[1 + 0.00386(0 - To) + B(0 - To)2]

Simplifying and solving for To, we get:

To ≈ 0.95°C

Resistance is a property of materials that opposes the flow of electrical current. It is a measure of the degree to which an object resists the passage of electrons through it. Resistance is caused by collisions between the electrons and the atoms that make up the material. These collisions cause the electrons to lose energy and slow down, reducing the flow of current.

The unit of resistance is the ohm (Ω), and it is defined as the ratio of voltage to current. Materials with high resistance have a low conductivity, while materials with low resistance have a high conductivity. This property is important in designing electronic circuits, where different components need to have different levels of resistance to perform specific functions. Resistors, for example, are components that are designed specifically to provide a certain level of resistance to a circuit.

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A bar magnet falls under the influence of gravity along the axis of a long copper tube. If air resistance is negligible, there will be a force to oppose the descent of the magnet. The magnet will reach a terminal velocity. Here's why:

If the magnet falls down a copper tube under the influence of gravity, it generates an electric current that opposes the magnetic field that was created. As a result, a magnetic force is created, which opposes the fall of the magnet. As a result, there is a force opposing the descent of the magnet.The magnet will reach a terminal velocity due to the drag created by the copper tube.

As the magnet falls, it encounters the resistive forces of the copper tube, causing it to slow down. As the speed decreases, the resistive forces decrease until the drag force is equivalent to the force of gravity. The magnet then reaches a steady state called the terminal velocity. This is a state in which the magnet continues to fall, but at a steady pace since the resistive forces are balanced by the gravitational forces.

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The structure described by the scientist, which is an oily sphere with an inner fluid, is most likely a lipid vesicle.

Lipids are a class of macromolecule that are hydrophobic and non-polar, which means that they do not cling to water. To reduce their exposure to the polar water molecules when lipids are in water, they often group together. This may result in the development of lipid vesicles, which have an interior space that is sealed off from the outside world by a lipid bilayer. Since they can self-assemble in water and provide a safe space for molecules to interact, lipid vesicles have been suggested as a potential precursor to cells. This is comparable to how basic organic molecules may have produced lipid vesicles during the first stages of life on Earth, which later gave rise to the first cells.

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The given statement "If two identical wires carrying a certain current in the same direction are placed parallel to each other, then they will experience a force of repulsion" is true. This can be explained through Lenz's law.

Two parallel wires which are carrying the same magnitude of current in the same direction experience a force of repulsion due to the electric currents in each of the wire which are creating a magnetic field in the same direction. This force of repulsion is known as the Lenz's Law.

When two identical wires are carrying a certain magnitude of electric current in the same direction and these are placed in parallel to each other, then they will experience a force of repulsion. This is due to the principle of the electromagnetic force and Lenz's law. When the two current-carrying wires are kept near each other, then they exert force on each other, and that force is called as the force of repulsion or the force of attraction depending on the direction of the current flowing through the wire. The direction of the force is given by the Fleming's left-hand rule, which is the most common way to determine the direction of the force in such cases.

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Нам не дано коэффициент трения, значит, можно не учесть силу трения. От этого, по второму закону Ньютона, F=ma=5×20=100 Н.

И это всё!

Answer: 7.17

Explanation:

Maximum height reached by Kangaroo H=2.62

Final velocity at the maximum height v=0

Acceleration due to gravity   g=−9.8 m/s2    

Using   v2−u2=2gH∴   0−u2=2(−9.8)(2.62)

⟹ u=2(9.8)(2.62)​=7.17 m/s

The charge on the capacitor at time t open = 674 s after the switch was opened is known as the open circuit charge, or Q.

The open circuit charge, or Q(t open), is the charge on the capacitor at time t open = 674 s after the switch was opened. Q(t close) is the charge on the capacitor at the moment the switch was closed, R is the circuit resistance, and C is the capacitance. This charge can be calculated using the equation,

Q(t open) = Q(t close)e^(-RC t open)

Q(t open) = Q(t close)e^(-RC674 s),

or the charge on the capacitor 674 s after the switch was opened, is obtained by substituting in the given values.

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a) The distribution of X: X-N(129.77,2.26),

b) the proportion of her laps that are completed between 131.69 and 134.04 seconds 0.1670,

c) the fastest 4% of laps are under 126.1965 seconds,

d) the middle 70% of her laps are from seconds 127.5323 to 131.0277 seconds.

a. The distribution of X is the normal distribution with a mean of 129.77 seconds and a standard deviation of 2.26 seconds. Therefore, the distribution of X is X - N(129.77, 2.26).

b. The area between 131.69 and 134.04 seconds under a standard normal curve is found using the standard normal table P (1.05) = 0.8531P (1.71) = 0.9564

Therefore, the proportion of laps completed between 131.69 and 134.04 seconds is

P(131.69 ≤ X ≤ 134.04) = P[(131.69 - 129.77)/2.26 ≤ Z ≤ (134.04 - 129.77)/2.26]

= P(0.8496 ≤ Z ≤ 1.8814) = P(Z ≤ 1.8814) - P(Z ≤ 0.8496)

= 0.9693 - 0.8023

= 0.1670

Therefore, the proportion of laps that are completed between 131.69 and 134.04 seconds is 0.1670.

c. The value corresponding to the lowest 4% is found: P (z) = 0.04. The value of z corresponding to the lowest 4% is obtained as follows:

z = P−1(0.04) = -1.7507

So, the number of seconds that the fastest 4% of laps are under is:

x = μ + zσ = 129.77 - (1.7507)(2.26)

= 126.1965

Therefore, the fastest 4% of laps are under 126.1965 seconds.

d. We know that z corresponding to the lowest 15% is -1.036 and that z corresponding to the highest 15% is 1.036.

Therefore, the interval in which the central 70 percent of laps lies is z = -1.036, 1.036

z = P(X) - P(X) = P(z ≤ X) - P(z ≤ X) = P(z ≤ -1.036) - P(z ≤ 1.036)

= 0.1492 - 0.8513

= -0.7021

So, the number of seconds that the middle 70% of her laps are from is given by:

x = μ + zσ = 129.77 + (-0.7021)(2.26) = 127.5323 and

x = μ + zσ = 129.77 + (0.7021)(2.26) = 131.0277

Therefore, the middle 70% of her laps are from seconds 127.5323 to 131.0277 seconds.

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