# Excape velocity

1. Apr 23, 2005

### UrbanXrisis

An object is fired from the earth's surface with a speed of 2.00x10^4 m/s. What will its speed be when it is very far from the earth? (neglect friction)

so... what I did was find the excape velocity of the earth, which is 11190.7 m/s then subtract that from the initial speed.

my teacher said that when and object is fired at excape velocity, it will slow down to 0m/s when it is at an infinite distance from the earth. so if I just subtract 2.00x10^4-11190.7 then that will give me the velocity it should have, which is 8806 m/s, but my book says 1660 m/s. What did I do wrong?

2. Apr 23, 2005

### VietDao29

The Gravitational Force can slow an object with an escape velocity to 0 at "infinity". Can you find out the work done by Earth when that object reach "infinity"?
Hint:
$$\Delta KE = \sum{Work}$$
Where
$$\Delta KE = -\frac{1}{2}mv^{2}_{esc}$$
So when an object is at "infinity", the Earth will do that amount of work on an object.
Use $\Delta KE = \sum{Work}$ again to find the final velocity when that object is very far from Earth.
Viet Dao,

Last edited: Apr 23, 2005
3. Apr 23, 2005

### OlderDan

Making the previous hint a bit more explicit. The work done is incorporated in the potential energy. The statement made by your teacher is equivalent to saying that escape velocity is the velocity needed to give the object a total energy (kinetic plus potential) of zero. By definition the potential energy is zero at infinity. That will let you figure out the initial potential energy in your problem