Question

From what height should an object be dropped on the Moon so that it's final velocity upon reaching the surface is the same as when droppped from a height of 20 m on the Earth?
Take 'g' on Earth = 10 ms${}^{-2}$.

• A. 180 m
• B. 60 m
• C. 80 m
• D. 120 m

Answer 1

The correct option is D 120 m

Given: H${}_{earth}$ = 20 m, g${}_{earth}$ = 10 ms${}^{-2}$

Solution: We know that,
$g_{moon}=\frac{1}{6}{g}_{earth}$

Hence, using 3rd equation of motion,
v${}^2$ - u${}^2$ = 2as

For Earth,
v${}^2$ = 0 + 2 x 10 x 20 = 400
v = 20 ms${}^{-1}$

For moon,
${20}^2=0+2\ast \frac{10}{6}\ast H_{moon}$
H${}_{moon}$= 20 x 6 = 120 m