(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hint:Disregard any dissipative effects of the atmosphere of the planet.

A projectile is launched from the surface of a planet (mass M, radius R)

with a launch speed equal to 60 percent of the escape speed for that planet.

The projectile will rise to a maximum height and fall back to the surface of

the planet.

What will be the ratio of its maximum height above the surface to the radius of the

planet, h/R?

2. Relevant equations

escape speed:

KE = E(gravity)

1/2 mv^2 = (GMm)/R

F/m = a

a(gravity) = GM/R^2

3. The attempt at a solution

1/2 mv^2 = (GMm)/R

v(escape) = (2GMm)/R

v=sqrt((2GM)/R)

vi = 0.6 sqrt((2GM)/R)

vf^2 = vi^2 - 2gh

0 = 0.72GM/R - 2(GM/R^2)h

2(GM/R^2)h = 0.72GM/R

h/R = 0.36

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Ratio of max height of a projectile to planet radius

**Physics Forums | Science Articles, Homework Help, Discussion**