Question

On the earth, an astronaut can safely jump to the ground from a height of 1.2 m ; her velocity when reaching the ground is slow enough to not cause injury. From what height could the astronaut safely jump to the ground on the moon?

Answer 1

We use the kinematic equation,

$v^{2} = u^{2} +2gh$

Here, u is initial velocity, and v is final velocity, g is acceleration due to gravity and h is maximum height.

The velocity of the astronaut reaching the ground from h is

$v=\sqrt{2 g_{earth} \times h_{earth} }$

Here, u = 0.

Similarly, for moon

$v=\sqrt{2 g_{moon} \times h_{moon} }$.

Take,  $g_{earth}  = 9.8 m/s^2$ and $g_{moon} = 1.625 \ m/s^2$.

For safe jump to the ground, the velocity should be same.

Therefore,

 $\sqrt{2 g_{earth} \times h_{earth} } = \sqrt{2 g_{moon} \times h_{moon} } \\\\

[tex]9.8  m/s^2 \times 1.2 \ m = 1.625  m/s^2 \times h_{moon} \\\\ h_{moon} = \frac{11.76}{1.625} = 7.2 \ m$

Thus, the astronaut safely jump to the ground on the moon from height 7.2 m.