Question

An object of mass m is dropped from a height h above the surface of a planet of mass M and radius R. Find the speed of the object when it hits the planet surface. Enter your answer as an expression in terms of m, M, R, h and the universal constant of gravity G.

Answer 1

`v=\sqrt{(2GMh)/(R^(2))}`

Step-by-step explanation:

mass of object = m

Mass of planet = M

Radius of planet = R

Height = h

Let the speed of the object as it hits the earth's surface is v.

the value of acceleration due to gravity

g = G M / R^2

where, g is the universal gravitational constant.

Use third equation of motion

`v^(2)=u^(2)+2gh`

where, u is the initial velocity which is equal to zero.

So,
`v^(2)=0 + 2 * (GM)/(R^(2))* h`

`v=\sqrt{(2GMh)/(R^(2))}`