Gravitational Potential Energy

[slayer16]

Homework Statement

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.

Homework Equations

Gravitational potential energy
Escape Speed
Conservation of Mechanical Energy

The Attempt at a Solution

I got part A, but I do not know how to set up part b correctly.

 

[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?

 

[slayer16]

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

What is the expression for Gravitational potential energy?

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?

 

[rock.freak667]

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?

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.