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squirrelschaser
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Homework Statement
Planet 1 has mass 3M and radius R, while Planet 2 has mass 4Mand radius 2R. They are separated by center-to-center distance 8R. A rock is placed halfway between their centers at point O. It is released from rest. Ignore any motion of the planets.
The rock is released from rest at point O. Derive an expression for the speed v with which the rock crashes into a planet.
Homework Equations
KE = 1/2 *m *v^2
PE = GMm/R
The Attempt at a Solution
(3GMm/4R) -4GMm/4R = .5mV^2 + (3GMm/6R) - (4GMm/2R)
-1GMm/4R = (.5mV^2) - (3GMm/2R)
5GMm/4R = .5mV^2
5GMm/2R = mV^2
5GM/2R = V^2
(2.5GM/R)^(1/2) = V (My answer)
(1.5GM/R)^(1/2) = V (Actual answer)