Question

The gravitational attraction on the surface of the Moon (lunar surface) is about `1/6`th of that on the surface of the Earth. An astronaut can throw a ball up to a height of 8 m from the surface of the Earth. How far up will the ball thrown with the same upward velocity travel from the surface of the Moon?

Answer 1

Given,

Height reached on Earth, h_E = 8 m

Gravitational attraction on the Moon, g_M = `1/6"g"_"E"`

On both the Earth and the Moon, the ball is thrown with the same upward velocity, u. The velocity drops to zero at the highest point.

Using v² = u² – 2gh, with v = 0,

`h = (u^2)/(2g)`

The height h is inversely proportional to g since u is the same in both situations.

The height h is inversely proportional to g since u is the same in both situations.

`(h_M)/(h_E) = (g_E)/(g_M) = (g_E)/(1/6 g_E) = 6`

h_M = 6 × h_E = 6 × 8 = 48 m

As a result, the ball will rise from the Moon's surface to a height of 48 m.