Question

Suppose you are visiting a planet in a distant part of the galaxy. To determine the acceleration due to gravity on this planet, you drop a small rock from a height of 55m. The rock strikes the ground 1.9s later. How many times greater is the acceleration due to gravity on this planet than on earth.

Answer 1

Answer on Question #69941, Physics / Other

Suppose you are visiting a planet in a distant part of the galaxy. To determine the acceleration due to gravity on this planet, you drop a small rock from a height of 55m. The rock strikes the ground 1.9s later. How many times greater is the acceleration due to gravity on this planet than on earth.

Solution:

The kinematic equation is

$$h = v _ {0} t + \frac {a t ^ {2}}{2}$$

The initial velocity

$$v _ {0} = 0$$

The acceleration due to gravity is

$$a = \frac {2 h}{t ^ {2}}$$

Substituting

$$a = \frac {2 \times 55 \, m}{(1.9 \, s) ^ {2}} = 30.47 \, m/s ^ {2}$$

The acceleration due to gravity at the surface of Earth is represented as g. It has a standard value defined as 9.81 m/s².

The acceleration due to gravity on this planet is

$$\frac {30.47}{9.81} = 3.1$$

times greater than on earth.

Answer: 3.1

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