Distance a particle travels if launched tangentially into space

[aheizler]

Homework Statement

A non-rotating spherical planet has mass M and radius R. A particle is fired off from the surface with a speed equal to 3/4 the escape speed. Calculate the farthest
distance it reaches (measured from the center of the planet) if it is fired off tangentially.

Homework Equations

GPE = G*M*m*((1/R) - (1/d))
KE = ½*m*Ve²

The Attempt at a Solution

I did this problem correctly when the problem stated that the particle is fired off radially (d=R*(16/7)), but I don't know what changes when the particle is fired tangentially.

 

[nickjer]

When fired radially you assume the maximum distance is when the velocity goes to 0. But when fired tangentially (or throwing a ball in the air at an angle), the maximum height doesn't have 0 total velocity (so KE_final is not 0). The maximum height will have 0 radial velocity, but can still have tangential velocity.

So you will need to use conservation of angular momentum to help solve this.