Question

A rock falls from rest a vertical distance of 0.72 meter to the surface of a planet in 0.63 second. What is the magnitude of the acceleration due to gravity on the planet?

Answer 1

The magnitude of the acceleration due to gravity on the planet is calculated using the kinematic equation and the given distance and time. The result is an acceleration due to gravity of 3.63 m/s² on that planet.

Step-by-step explanation:

To calculate the magnitude of the acceleration due to gravity on the planet based on the information provided that a rock falls from rest a vertical distance of 0.72 meters in 0.63 seconds, we use the kinematic equation:

s = ut + ½ at²

Where:

• s is the distance the object travels (0.72 meters),
• u is the initial velocity (0 meters per second, since the rock falls from rest),
• t is the time taken (0.63 seconds), and
• a is the acceleration due to gravity, which we need to find.

Rearranging the kinematic equation to solve for a, we have:

a = 2s / t²

Substituting the given values:

a = 2 * 0.72 m / (0.63 s)²

a = 1.44 m / 0.3969 s²

a = 3.63 m/s²

Therefore, the magnitude of the acceleration due to gravity on the planet is 3.63 m/s².

Answer 2

s = 0.72 m, t=0.63 s
s = a · t² /2
0.72 m = a · (0.63 s )² / 2
a · 0.3969 s² = 1.44 m
a = 1.44 m : 0.3969 s² = 3.628 m/s²
The magnitude of the acceleration due to gravity on the planet is 3.628 m/s²