# Escape speed

## Homework Statement

By considering the gravitational potential energy of an object at the surface , find an expression for the escape speed from the surface and determine its value.

GPE= mgh

## The Attempt at a Solution

KE= 1/2* m * v^2

GPE= mgh

GPE+ KE = 0

mgh = - 1/2 * m * v^2
gh= - 1/2 * v^2

v^2= -2gh

v= sqare root of (-2gh)

this is the escape velocity...

Dick
Homework Helper
You've computed velocity needed to reach a height h in a uniform gravitational field. Is that the same concept as 'escape velocity'?

HallsofIvy
Homework Helper
You also appear to be assuming gravitational force is constant. If that were true, there would be no "escape velocity". It is impossible to "escape" a constant force!

Well if ur looking for escape velocity....it should be$$\sqrt{\frac{2GM}{R}}$$

thanks for the info...
so how shall i start off instead

you shud use the work energy theorem

Last edited:
Dick