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Distance a particle travels if launched tangentially into space

  • Thread starter aheizler
  • Start date
  • #1
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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.
 

Answers and Replies

  • #2
674
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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.
 

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