Answer to Question #85554 in Mechanics | Relativity for ash

Question

In an experiment to discover the acceleration due to gravity, a rock was dropped on the planet Zeus.
If it fell a distance of 15 m in 5 s, the acceleration of gravity on Zeus is

Answer 1

Assuming that a rock was dropped without the initial velocity, one can use the following relation between the distance, acceleration and time of flight:

$$H=\frac{g_{Z} t^2}{2},$$

where g_Z is the acceleration of gravity on Zeus. Deriving its value from the exression above, one can obtain:

$$g_Z = \frac{2 H}{t^2}.$$

Substituting the numerical values, we get:

$$g_Z = \frac{2 \cdot 15}{5^2} = 1.2 \, m/s^2$$

Answer: 1.2 m/s²