Question

A projectile is launched on the Earth with a certain initial velocity and moves without air resistance. Another projectile is launched with the same initial velocity on the Moon, where the acceleration due to gravity is one sixth as large. How does the range of the projectile on the Moon compare with that of the projectile on the Earth?

(a) It is one-sixth as large.

(b) It is the same.

(c) It is$\sqrt{\mathbf{6}}$ times larger.

(d) It is 6 times larger.

(e) It is 36 times larger.

Short answer

The range of a shot on the Moon is 6 times greater than that of a projectile on Earth.

Option (d) is true

Step-by-step solution

Step 1: Define maximum height of the projectile

The maximum horizontal distance that the projectile can reach after the launch, is called the range of the projectile. If the initial velocity and the angle of launch, with horizontal, are same, the range of projectile is inversely proportional to the acceleration due to gravity.The maximum horizontal distance that the projectile can reach after the launch, is called the range of the projectile. If the initial velocity and the angle of launch, with horizontal, are same, the range of projectile is inversely proportional to the acceleration due to gravity.

Explanation for correct option

The initial velocity of the two projectiles be$v_i$

The Range of the projectile is,$R=\frac{v_i^2\sin \text{2}\theta }{g}$

A projectile is launched with a given initial velocity on Earth, and another projectile is released with the same initial velocity on the Moon. The angle of launch are also same on both the moon and earth. As, the acceleration due to gravity on the Moon is one-sixth of that on Earth. $g_M=\left(\frac{1}{6}\right)g_E$

As a result, the range of a shot on the Moon is 6 times greater than that of a projectile on Earth.

Option (d) is true.