If a ball is released from chin height on a planet with g = 30 m/s², how does its behavior differ from that on Earth?

When a ball is released from chin height on a planet where the acceleration due to gravity (g) is greater than that on Earth, which is approximately 9.81 m/s², the ball will experience a stronger gravitational force pulling it downward. Because of this increased gravity, the time it takes for the ball to fall to the ground will be shorter compared to its fall on Earth.

The relationship between the distance fallen and the time taken is governed by the equations of motion. On a planet with a higher g value, the equation for the distance fallen can be expressed as:

[ d = \frac{1}{2} g t^2 ]

This formula shows that the distance is proportional to the acceleration due to gravity and the square of the time. Consequently, for the same release height, a greater value of g will result in a smaller time, making it take less time for the ball to reach the ground.

Thus, the ball released from chin height on a planet with g = 30 m/s² will indeed take less time to return to the ground than it would on Earth.