Question

An astronaut stands on the top of a crater on the moon. He drops a rock from the top of the crater. Calculate the fraction of its speed to the final impact speed when it is midway between the top and bottom of the crater.

• A. $\frac{1}{4\sqrt{2}}$
• B. $\frac{1}{4}$
• C. $\frac{1}{2\sqrt{2}}$
• D. $\frac{1}{\sqrt{2}}$

Answer 1

Answer: (D)

$\frac{1}{\sqrt{2}}$

Let the total drop distance be $h$.

Speed of rock when dropped through half the height:

$v_1=\sqrt{2g\times \frac{h}{2}}$

$g$ : acceleration due to gravity on the planet

Speed of rock when dropped through full height

$v_2=\sqrt{2gh}$

Now,

$⟹\frac{v_1}{v_2}=\frac{1}{\sqrt{2}}$