As part of an experiment on Mythbusters, a car was dropped from a crane 131 m (approximately 430 ft) above the
ground. If you assume there is no air resistance,
(a) how long would it take for the car to reach the ground?
(b) with what velocity will the car hit the ground?

Formula connecting acceleration, initial speed, final speed and time.

v=u+at,

v2=u2+2as,

s=ut+1/2at2.

For motion on a straight line with constant acceleration, there are five common formulas. The formulas are provided in terms of the initial velocity (u), final velocity (v), displacement (x), acceleration (a), and time (t).

The following equation can be used to determine distance from acceleration: D = v*t + 1/2*a*t2. where an is the acceleration, t is the passage of time, and v is the velocity.

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Echo

Explanation:

It is termed as Echo. Echo is a reflection of sound that arrives at the listener with a delay after the direct sound.

It would take the star 2 seconds to lose all it's mass.

I got this by dividing 12.044×10⁴⁶ by  6.022×10²³

0.212 m/s²  is the average acceleration of the treadmill.

during this period

initial velocity, u = -1.2 m/s

time= 25 min

final velocity, v=  −6.5 m/s

acceleration = (v-u)÷ t

acceleration =5.3/25

acceleration =0.212 m/s²

The rate at which an item changes its velocity is known as acceleration, a vector variable. If an object's velocity is changing, it is accelerating. A moving object can occasionally alter its velocity by the same amount every second. a moving object that changes its speed by 10 m/s per second. Since the velocity is changing by a fixed amount every second, this is known as a constant acceleration. It is important to distinguish between an item with a constant acceleration and one with a constant velocity. Be not deceived! An object is accelerating if its velocity is changing, whether by a fixed amount or a variable quantity. Additionally, a moving item with a constant speed is not accelerating.

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(a) The mechanical energy of the particle at the origin is 0 J.

(b) The mechanical energy of the particle at 4 m is 625 J.

(c)  The particle’s velocity at 1.0m is 17.32 m/s.

The mechanical energy of the particle is the total energy of the particle due to its motion and position above the ground such as kinetic energy and potential energy.

E = P.E + K.E

E = mgh + ¹/₂mv²

where;

at the origin, the displacement of the particle is zero and the velocity of the particle is zero.

E = (2 x 9.8 x 0) +  ¹/₂(2)(0)²

E = 0 J

The acceleration of the particle is calculated as follows;

F = ma

a = F/m

where;

a = (300)/2

a = 150 m/s²

The velocity of the particle at distance 4 m is calculated as follows;

v² = u² + 2as

where;

v² = (5)² + 2(150)(2)

v² = 625

v = √625

v = 25 m/s

E = ¹/₂mv²

E = ¹/₂(2)(25²)

E = 625 J

The particle's velocity at 1 m is calculated as follows;

Apply the principle of conservation of energy;

Work done by force = kinetic energy of the particle

Fd = ¹/₂mv²

where;

300 x 1 = ¹/₂(2)v²

300 = v²

v = √300

v = 17.32 m/s

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1.125 joule work done does air resistance do on the ball

work done= kinetic energy= mΔv²/2

m=0.25kg

Δv=3 m/s

work done= mΔv²/2

work done=-0.25×9÷2

work done=-1.125 joule

When an item is moved across a distance by an external force, at least a portion of that force must be applied in the direction of the displacement. This is known as work done in physics. By multiplying the length of the path by the component of the force operating along the path, work may be calculated if the force is constant. The work W is equal to the force f times the distance h, or W = mgh, to mathematically describe this idea. The work is W = mas if the force is applied at an angle of to the displacement.

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Answer:

A) 1000 kg

Explanation:

vf = vi + at

0 = 20 + (a)(10)

a = -2.0 m/s^2

F = ma

2000 = (m)(2)

m = 1000 kg

Answer:

Weight is a measure of the force of gravity pulling down on an object. It depends on the object's mass and the acceleration due to gravity

Explanation:

The net work done on the block over the given distance is 39.4d (joules)

The net work done on the block over the given distance is calculated by applying the following equation as shown below:

W(net) = F(net) x d where;

F(net) = F - μmgcosθ where;

F(net) = 50 N - (0.25 x 5 x 9.8 x cos30)

NF(net) = 50 N - 10.6 NF(net) = 39.4 N

The net work done on the block over the given distance is calculated as: W = 39.4 N x dwhere;

d is the distance moved by the block = length of the incline

W = 39.4d (joules)

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Answer:

seismic waves

Explanation:

The option that  would increase the mechanical advantage of a lever is option A. Moving the fulcrum closer to the output force.

Mechanical advantage quantifies a lever's effectiveness (how easy it is to lift the load). - When compared to the distance between the load (resistance) and the fulcrum, the advantage relies on the distance between the effort and the latter (effort arm) (resistance arm).

Note that in Levers of Class 1:

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It takes a black hole an astonishingly long time to convert all of its mass into energy via Hawking radiation. A googol, or 10100 years, would be required for a supermassive black hole to completely vanish.

A black hole radiates, losing mass as it does so and beginning to release more radiation, which accelerates the evaporation of the black hole. It eventually contracts to a size close to the Planck mass, where its Schwarzschild radius and DeBroglie wavelength coincide.

Sagittarius A* 1087 years for Ton 618, the biggest black hole ever detected, and Sagittarius A* 1087 years for Sagittarius A* to evaporate from Hawking radiation It would take more than 10100 years for it to evaporate away (weighing a staggering 66 billion solar masses).

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As per Drag theory , one possible explanation is v=0 that means velocity of earth relative to ether is zero.

For t1=t2, as per equation

[tex]t1=2l/c [ 1 + v^{2} /c^{2} ]\\t2= 2l/c [ 1 + v^{2} /2c^{2} ][/tex]

Then there is no relative velocity between earth and ether. In other words the ether is dragged with the motion of earth with the same velocity as the earth. However if this explanation is acceptable for there should be no aberration of light. Even if the ether is considered to be dragged partially , the absence of fringes shift and value of aberration cannot be explained simultaneously.

It has been verified by experiments that newton's frame of reference taking stars to be fixed , is an inertial one , while the other one i.e. reference frame fixed to earth  is not an inertial frame. Since the earth rotates about its axis as well as round the sun.

Even Galilean Transformation equations explain the structure of inertial frames.

For example - Length of a rod is invariant under Galilean transformations.

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Answer: D: 136 N

..

..

a. ) The period is  1/frequency = 5sec / 9 cycles = 0.555 seconds

b.) the seconds out of phase with the displacements shown would graphs of the velocity and acceleration be 5/18 (0.2777...) sec delayed with respect to displacement

c.) Gravity = (324 π²) (0.2) / 25  =  25.582 m/sec²

What is gravity?

Gravity is defined as a fundamental interaction which causes mutual attraction between all things with mass or energy.

Solving for  the acceleration due to gravity on the surface of the planet, we have the following:

For small swing angles, the period of an ideal pendulum anywhere is

                T = 2pi √(length / local gravity)  .

The astronaut has already done the pendulum and transmitted the data to us, so

we can use his data and this formula to calculate the local gravity where he is located

          P = 2pi √(length / local gravity)

           5/9 sec = 2π √(0.2m / gravity)

        √(0.2m / gravity) =  5/9sec / 2π

Take the reciprocal of each side:    √(gravity) / √(0.2) =  18π / 5

Multiply each side by  √(0.2):    √(gravity) = 18π √(0.2) / 5

Square both sides:      Gravity = (324 π²) (0.2) / 25  =  25.582 m/sec²

The value gotten is about  2.608 times  the Earth's gravity.  

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(a) The speed of the student at the bottom of the hill is 15.34 m/s.

(b) The speed of the student at the presence of friction force is 11.88 m/s.

The speed of the student at the bottom of the hill is calculated by applying the principle of conservation of energy as shown below.

Kinetic energy at the bottom hill = potential energy at maximum height

¹/₂mv² = mgh

where;

v² = 2gh

v = √2gh

v = √(2 x 9.8 x 12)

v = 15.34 m/s

The speed of the student at the presence of friction force is calculated as;

Kinetic energy at the bottom hill + work done against friction  = potential energy at maximum height

¹/₂mv² + μmgh = mgh

¹/₂v² + μgh = gh

v²  +  2μgh = 2gh

v² = 2gh - 2μgh

v² = (2 x 9.8 x 12) - (2 x 0.4 x 9.8 x 12)

v² = 141.12

v = √141.12

v = 11.88 m/s

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Answer:

1039 N

Explanation:

The 'x' components of their pulling forces = the force of friction:

2 x 600 cos 30 = 1039 N

Answer: C Adding salt to water increases the boiling point and decreases the freezing point

Explanation:

Stars that have a mass greater than the 1.4 solar masses or the Chandrasekhar limit will not become white dwarfs.

The Chandrasekhar limit is the maximum mass that a stable white dwarf star can have. It was noted by E.C. Stoner and Willhelm Anderson in their works, and they gave it the name Subrahmanyan Chandrasekhar in honour of the Indian astronomer who made important, independent findings for enhancing calculation accuracy.

The limit was first disregarded by the scientific community since it would have supported the existence of black holes (technically unrealistic at this turn-off time). The white dwarf stars resist the gravitational collapse of the black hole due to the pressure of electron degeneration.

The Chandrasekhar limit is established at a mass where the gravitational field's self-attraction cannot be balanced by the pressure from electron decay.  The limit that has been established these days is 1.39 solar mass.

Hence, Stars that have a mass greater than the 1.39 solar masses or the Chandrasekhar limit will not become white dwarfs.

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The total current that is drawn from the mains supply is 5 A.

The term current has to do with the flow of charges in a circuit. Now we have been told that A set of lights consists of 20 lamps connected in series to the 230 V mains electricity supply. It was also said in the question that when the lights are switched on and working correctly, the current through each lamp is 0.25 A.

Now we have the following information;

Current passing through each lamp = 0.25 A

Number of lamps = 20 lamps

Hence;

Total current = 0.25 A * 20

= 5 A

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42 times must he repeat this exercise to burn off the energy in one slice of pizza.

What is energy?

Energy is the ability or capability to do tasks, such as the ability to move an item (of a certain mass) by exerting force. Energy can exist in many different forms, including electrical, mechanical, chemical, thermal, or nuclear, and it can change its form.

Energy burn by the weightlifter = potential energy

Potential energy = mgh

Potential energy = 25.(9.8)(0.50)

Potential energy = 122.5 Joule.

Assume 25% of efficiency so energy burn = 122.5*25/100

energy burn = 30.625 joule

Number of times = 1260/30.625

Number of times = 42 times.

42 times must he repeat this exercise to burn off the energy in one slice of pizza.

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Answer:

The force of friction and air resistance slow down the movement of the bus.

c) A forse is changing the motion of the bus

Answer:

35.2 AU

Explanation:

Kepler's Third Law states that the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.

[tex]\boxed{T^2 \propto a^3 \implies T^2=ka^3}[/tex]

Kepler's Third Law

[tex]T^2=\dfrac{4 \pi^2}{GM}a^3[/tex]

where a is the semi-major axis of the ellipse.

If expressed in the following units:

then:

[tex]\implies\dfrac{4 \pi^2}{GM}=1[/tex]

Therefore Kepler's Third Law can be expressed as:

[tex]\boxed{T^2=a^3}[/tex]

Given:

From inspection of the given diagram:

[tex]\implies 2a=x+0.57[/tex]

[tex]\implies a=\dfrac{x+0.57}{2}[/tex]

Substitute these values into the equation and solve for x:

[tex]\implies (75.6)^2=\left(\dfrac{x+0.57}{2}\right)^3[/tex]

[tex]\implies (75.6)^\frac{2}{3}=\dfrac{x+0.57}{2}[/tex]

[tex]\implies 2(75.6)^\frac{2}{3}=x+0.57[/tex]

[tex]\implies x=2(75.6)^\frac{2}{3}-0.57[/tex]

[tex]\implies x=35.1883819...[/tex]

[tex]\implies x=35.2\; \text{AU}[/tex]

Answer: 2 Forces

Explanation:

1. Normal force- object is on a surface

2. Weight

The work done by the elevator over the 55 meters is easily calculable: W = mgh = (2400)(9.8)(55) = 1293600Joules. The total time of the trip can be calculated from the velocity of the elevator: t = x/v=55/18.9 = 2.91. Thus the average power is given by: P =W/t=1293600/2.91=444536   Watts

vf = vi + at = 2 m/s + (4 m/s²) (2 s) = 10 m/s

0.99 joule must the work done by friction to stop the box.

m=87g

k=82N/m

x=11cm=0.11m

spring force=kx

spring force=82N/m×0.11m

spring force=9.02 N

work done= Fx

work done=9.02 N×=0.11m

work done=0.99 joule

When an item is moved across a distance by an external force, at least a portion of that force must be applied in the direction of the displacement. This is known as work done in physics. By multiplying the length of the path by the component of the force operating along the path, work may be calculated if the force is constant. The work W is equal to the force f times the distance h, or W = mgh, to mathematically describe this idea. The work is W = mas if the force is applied at an angle of to the displacement.

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The change in angular velocity for the object from t=1s to t=3s is most nearly  24 rad/s².

The change in the angular velocity of the object is the angular acceleration of the object and the magnitude is calculated as follows;

α = Δω/Δt

where;

α = at³ - w₂

α = d(at³ - w₂)/dt

α = 3at²

The given parameters;

α = 3(2)(2)²

α = 24 rad/s²

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Answer:

Charge q = 37.27 micro coulombs

Explanation:

Given:

q₁ = q₂ = q

r = 2.5 m

F = 2.0 N

________

q - ?

Coulomb's law:

F =k·q₁·q₂ / r² = k·q·q / r² = k·q² / r²

Charge:

q = √ (F·r² / k)

q = √ (2·2.5² / (9·10⁹) ≈ 37.27·10⁻⁹  C

or q = 37.27 micro coulombs

The correct answer is not 52, but !!! :))