Two racquets hit two tennis balls at the same speed and angle-one on the Earth and the other on the Moon. Because the acceleration due to gravity on the Moon is six times smaller than on the Earth, the ball on the Moon would travel
A) the same horizontal distance as on the Earth.
B) 6 times the horizontal distance on the Earth.
C) 36 times the horizontal distance on the Earth.
D) 1/6 times the horizontal distance on the Earth.
E) 1/36 times the horizontal distance on the Earth.

Question

Quizplus · Accepted Answer

The horizontal distance (range) a projectile travels is directly proportional to the square root of the acceleration due to gravity. Since the Moon's gravity is 1/6th that of Earth's, the range would be $\sqrt{6}$ times greater. However, because the time of flight is also affected (it increases as gravity decreases), the overall effect is that the ball travels 6 times the horizontal distance on the Moon compared to Earth.

Two Racquets Hit Two Tennis Balls at the Same Speed