A student wants to know how the motion of the rock would be different if it was thrown upward at 15m/s from a height of 100m above Earth's surface. In a clear, coherent, paragraph-length response that may also contain figures and/or equations, explain how the motion of the rock on Earth will be different from its motion on Planet X in terms of its maximum height above the ground, the speed at which it reaches the ground, the time in which it is in free fall, and its acceleration due to gravity.

Question

Physics

Ashtyn Andersen

28 February, 06:36

A student wants to know how the motion of the rock would be different if it was thrown upward at 15m/s from a height of 100m above Earth's surface. In a clear, coherent, paragraph-length response that may also contain figures and/or equations, explain how the motion of the rock on Earth will be different from its motion on Planet X in terms of its maximum height above the ground, the speed at which it reaches the ground, the time in which it is in free fall, and its acceleration due to gravity.

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Answers (1)

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Jared Luna · Answer 1

See explanation

Explanation:

Given:-

- The height from which rock is thrown, si = 100m

- The initial velocity, vi = 15 m/s

- Earth gravitational constant, g = 9.81 m/s^2

- Planet x gravitational constant = L

Find:-

explain how the motion of the rock on Earth will be different from its motion on Planet X in terms of its maximum height above the ground, the speed at which it reaches the ground, the time in which it is in free fall, and its acceleration due to gravity.

Solution:-

- Using third kinematic equation of motion in vertical direction. We have:

vf = vi + 2*a * (sf - si)

vf : Final velocity

a : Acceleration (free fall)

t : Time

s : Distance travelled

For maximum height (sf) - vf = 0:

sf = vi / 2*a + si

For earth, a = g

For planet, x = L

IF g > L, then maximum height reached on earth is less than that reached on planet X. IF g < L, then maximum height reached on Planet X is less than that reached on earth.

For speed (vf) at ground - sf = 0 and vi = 0:

vf = 2*a * (-si)

For earth, a = - g

For planet, x = - L

IF g > L, then maximum velocity reached on earth is more than that reached on planet X. IF g < L, then maximum height reached on Planet X is more than that reached on earth.

- Using second kinematic equation of motion in vertical direction. We have:

sf = si + vi*t + 0.5*a*t^2

sf : Final distance from ground

a : Acceleration (free fall)

t : Time

si : Initial distance from ground.

For time taken for entire journey (t) - (sf = 0):

0 = si + vi*t + 0.5*a*t^2

a*t^2 + 2*vi*t + 2*si = 0

t = [ - (2*vi) + / - √ (4vi^2 - 8*a*si) ] / 2a

For earth, a = g

For planet, x = L

IF g > L, then time taken reaching ground on earth is less than that reached on planet X. IF g < L, then time taken reaching ground on Planet X is less than that reached on earth.