Question

You read in a science magazine that on the Moon, the speed of a shell leaving the barrel of a modern tank is enough to put the shell in a circular orbit above the surface of the Moon (there is no atmosphere to slow the shell).What should be the speed for this to happen? Assume that the radius of the Moon is rM = 1.74×10^6m, and the mass of the Moon is mM = 7.35×10^22kg.

Answer 1

To solve this problem we will use the definition of the kinematic equations of centrifugal motion, using the constants of the gravitational acceleration of the moon and the radius of this star.

Centrifugal acceleration is determined by

$a_c = \frac{v^2}{r}$

Where,

v = Velocity

r = Radius

From the given data of the moon we know that gravity there is equivalent to

$a = 1.62m/s$

While the radius of the moon is given by

$r = 1.74*10^6m$

If we rearrange the function to find the speed we will have to

$v = \sqrt{ar}$

$v = \sqrt{1.6(1.74*10^6)}$

$v = 1.7km/s$

The speed for this to happen is 1.7km/s