Answer to Question #121147 in Classical Mechanics for Lizwi

Question

A rock, initially at rest with respect to Earth and located an infinite distance away is released and accelerates toward Earth. An observation tower is built 3 Earth-radii high to observe the rock as it plummets to Earth. Neglecting friction, how much greater is the rock’s speed when it hits the ground than its speed at the top of the tower?
1 : twice
2 : three times
3 : four times
4 : six times
5 : eight times
6 : nine times
7 : sixteen times

Answer 1

Answer is 1. Twice.

Since, initially energy is zero so when the rock hits the tower and Earth surface in two different cases,potential and kinetic energy are same thus

$$v_1^2=2g(4R)\\ v_2^2=2g(R)$$

Hence, conclude the ratio of

$$\frac{v_1}{v_2}=2$$