(adsbygoogle = window.adsbygoogle || []).push({}); 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 R_{0}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/r^{2}

F=ma

Angular Force : F=mv^{2}/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 v_{0}(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!

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# Homework Help: Particle Shot Tangentially to Surface

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