Answer to Question #316445 in Physics for john

Question

 

A 15-kg rock is dropped from rest on the earth and reaches the ground in 1.75s. When it is dropped from the same height on Saturn’s moon Enceladus, it reaches the ground in 18.6s. What is the acceleration due to gravity on Enceladus? 

Answer 1

The the free falling distance of a stone is given by

$$h=\frac{g_{Earth}t_{Earth}^2}{2}=\frac{g_{Enc}t_{Enc}^2}{2}$$

Hence, the acceleration due to gravity for Enceladus

$$g_{Enc}=\frac{g_{Earth}t_{Earth}^2}{t_{Enc}^2}$$

$$=\frac{9.81\times 1.75^2}{18.6^2}=0.0868\:\rm m/s^2$$