# Gravitational Potential Energy

1. Apr 11, 2010

### slayer16

1. The problem statement, all variables and given/known data
A rocket is accelerated to speed v=2√gR (where R is the radius of earth 6370 km) near Earth's surface surface and it then coasts upward. a) show that it wil escape from Earth. b) Show that very far from Earth its speed will be v=2√gR.

2. Relevant equations
Gravitational potential energy
Escape Speed
Conservation of Mechanical Energy

3. The attempt at a solution
I got part A, but I do not know how to set up part b correctly.

2. Apr 11, 2010

### rock.freak667

Remember the escape velocity is the velocity required to take the rocket from zero to infinity.

What is the expression for Gravitational potential energy?

3. Apr 11, 2010

### slayer16

PE=-GmM/R.
Also what do you mean when you say that the escape velocity is the velocity required to take the rocket from zero to infinity?

4. Apr 12, 2010

### rock.freak667

Gravitational PE is the energy required to take a point mass from infinity to a point. In this case you want a velocity to go from one point to infinity.

So in one case U is negative, so in the other case U is ?

And then this U should be changed into kinetic energy.