# Homework Help: Particle Shot Tangentially to Surface

1. Oct 19, 2011

### trevor51590

1. The problem statement, all variables and given/known data
A particle mass m is shot tangentially to the surface of a planet mass M radius R0 at 3/4 escape velocity. Determine the maximum radius the particle achieves from the center of the planet

2. Relevant equations
Escape Velocity : √(2GM/r)
Energy due to Gravity : -GMm/r2
F=ma
Angular Force : F=mv2/r
Conservation of Angular Momentum : L = r x p or L=mvr

3. The attempt at a solution
Honestly - the beginning of the attempt is where I'm having the issue = I can't decide if I want to use conservation of energy, conservation of angular momentum.

My thought process tells me alright, the particle is shot at a velocity v0 (3/4 escape velocity). This particle has a force acting upon it - the force due to gravity. I can picture exactly what happens to the particle. it won't be shot out fast enough to reach orbit, it reaches a maximum radius r, and then in a parabolic trajectory falls back down to the planet.

Quite honestly - I feel like it should be a very simple solution, I just can't wrap my head around it. Perhaps a tip to start will give me the momentum to find the solution.

Thanks!

2. Oct 20, 2011

### vela

Staff Emeritus
Centripetal force, not angular force (whatever that means).
L=mvr sin θ
You don't need to choose. You have to use both.
Elliptical trajectory, not parabolic.

3. Oct 20, 2011

### trevor51590

Thank you!

I used conservation of energy

1/2mvo2-C/A=1/2mvf2-C/A

For vf I used conservation of angular momentum to put it into terms of vi

Thanks again!