# Escape speed problem? or no?

1. Jan 24, 2005

### CinderBlockFist

A projectile if fired vertically from Earth's surface with an initial speed of 8.2 km/s. Neglecting air drag, how far from the survace of Earth will it go?

Well, I know that the escape speed of earth is 11.2 km/s. how would i go about solving this?

2. Jan 24, 2005

### learningphysics

It's not really an escape speed problem... Are you supposed to use the escape speed of the earth to solve it?

I'd use conservation of energy methods to solve it...

3. Jan 24, 2005

### vincentchan

use conservation of energy... your final velocity is 0...
the potential energy might a little bit tricky for you... just remind you... PE=mgh doesn't work in this case

PS. flying at 8.2km/s on the earth and ignore the air drag? that is so not realistic..

4. Jan 24, 2005

### CinderBlockFist

crap, i am looking at the formula y - yo = voysin(thetao) - gt, i dont know how to put it in this equation, can someone help me?

5. Jan 24, 2005

### clive

As vincentcahn told you before, you can't use the laws of motion in uniform gravitational field, because the projectil will go far away from the Earth' surface.

Use
$$E_p=-\gamma \frac{mM}{R+h}$$
for the potential energy
and
$$E_c=\frac{mv^2}{2}$$
for the kinetic one and apply the conservation of total energy.

6. Jan 24, 2005

### CinderBlockFist

ahhh, ok thanks clive!