Question

Astronauts on our moon must function with an acceleration due to gravity of 0.170g .If an astronaut can throw a certain wrench 15.0m vertically upward on earth, how high could he throw it on our moon if he gives it the same starting speed in both places?

Answer 1

PHYSICAL APPROCH:
You know that \[{V_f}^2 = {V_0}^2 - 2gh\]
The wrench is going upwards and when it reach the top of its path, Vf = 0. Therefore, you will have:
\[{V_0}^2 = 2gh    \rightarrow    V_0 = \sqrt{2gh}\]
Vo is the same in both places, so you will have:
\[{V_0}^2 = 2g_{earth}h_{earth}\] and \[{V_0}^2 = 2g_{moon}h_{moon}\]
then
\[g_{earth}h_{earth} = g_{moon}h_{moon}\]but
\[g_{moon}= 0.17g_{earth}\]
then
\[g_{earth}h_{earth} = 0.17g_{earth}h_{moon}\]\[h_{earth} = 0.17h_{moon}\]
Finally:
\[15 = 0.17h_{moon}\]
\[h_{moon} = 88.2 m\]

Mathematical Approach: Height is inversely proportional to gravity.
\[\frac{ g_{earth} } { g_{moon} } = \frac{ h_{moon} }{ h_{earth} }\]You will get the same height; h = 88.2m.

Answer 2

thank u so much