Question

The acceleration due to gravity on a planet is $1.96{\text{m/s}}^2$. If it is safe to jump from a height of $3\text{m}$ on the earth, the corresponding height on the planet will be

• A. $3\text{m}$
• B. $6\text{m}$
• C. $9\text{m}$
• D. $15\text{m}$

Answer 1

The correct option is D $15\text{m}$

Given that jump from a height of $3\text{m}$ on earth is safe.

So, corresponding this height, attained velocity will be

$v_1=\sqrt{2g_1{h}_1}$

This means, it will be safer to jump from a height on the other planet, if the velocity attained is the same. So, velocity due to corresponding height $h_2$ is given by

$v_2=\sqrt{2g_2{h}_2}$

So, for the safe jump,

$v_1=v_2\Rightarrow \sqrt{2g_1{h}_1}=\sqrt{2g_2{h}_2}$

$\Rightarrow g_1{h}_1=g_2{h}_2$

$\Rightarrow 9.8\times 3=1.96\times h_2$

$\Rightarrow h_2=5\times 3=15\text{m}$

Hence, option $\left(d\right)$ is correct.