Two rocks are thrown directly upward with the same initial speeds, one on earth and one on our moon, where the acceleration due to gravity is one-sixth what it is on earth. Part A If the rock on the moon rises to a height H, how high will the rock rise on the earth

The rock will rise H/6 units high on earth

Explanation:

In order to find the height to which rock rises, we use 3rd equation of motion. The 3rd equation of motion is as follows:

2gh = Vf² - Vi²

h = (Vf² - Vi²)/2g

where,

h = height

Vf = Final Velocity

Vi = Initial Velocity

g = acceleration due to gravity

ON MOON:

On moon:

h = H

Vf = 0 m/s (rock stops at highest point for a moment)

Vi = Vi

g = -(1/6) g (negative sign due to upward motion)

Therefore,

H = (0² - Vi²)/[-(2)(1/6)(g)]

H = 3Vi²/g

H/3 = Vi²/g   equation (1)

ON EARTH:

On earth:

h = ?

Vf = 0 m/s (rock stops at highest point for a moment)

Vi = Vi (same initial velocity)

g = - g (negative sign due to upward motion)

Therefore,

h = (0² - Vi²)/(-2g)

h = Vi²/2g

h = (1/2)(Vi²/g)

using equation (1), we get:

h = (1/2)(H/3)

h = H/6

whichever one it is, it's definitely not one that you included on the list you provided.

answer: the answer is a