Question

The weight of a person on a planet $\text{A}$ is about half that on the Earth. He can jump upto $0.4$ $\text{m}$ height on the surface of the Earth. How high can he jump on the planet $\text{A}$?

Answer 1

Since the weight of the person on the planet $\text{A}$ is half that on the Earth, the acceleration due to gravity there will be $\frac{1}{2}$ that on the Earth. Hence, he can jump double the height with the same muscular force.

The potential energy of the person will remain the same on the Earth and on planet $\text{A}$.
Thus, $m{g}_1{h}_1=m{g}_2{h}_2$
$g_1=$ $\text{acceleration due to gravity on Earth =}g$
$g_2=$ $\text{acceleration due to gravity on planet = A}$
$h_1=$ $\text{height on the surface of Earth}$
$h_2=$ $\text{height on the surface of planet A}$

$\text{If}$ $g_1=g$
$\text{then}$ $g_2=\frac{1}{2}g$
$h_1=0.4m$
$\text{Then}$ $h_2=\frac{g_1{h}_1}{g_2}=\frac{g\times 0.4}{\frac{g}{2}}$
or $h_2=0.4\times 2=0.8m$