NASA, when it sends probes to other planets, uses what is known as a gravitational slingshot. This is when a probe uses the gravitational potential energy a planet to gain kinetic energy. Even though the probe and the planet are not physically colliding, one can treat this problem as a perfectly elastic head on collision between the probe and the planet. Suppose the probe, with a mass of one millionth the mass of the planet, is approaching the planet initially at 269.8 m/s in the negative x direction and the planet is moving at 31.4 m/s in the positive x direction. What is the magnitude of the final velocity of the probe, in m/s, after the collision?

Question

NASA, when it sends probes to other planets, uses what is known as a gravitational slingshot.  This is when a probe uses the gravitational potential energy a planet to gain kinetic energy.  Even though the probe and the planet are not physically colliding, one can treat this problem as a perfectly elastic head on collision between the probe and the planet.  Suppose the probe, with a mass of one millionth the mass of the planet, is approaching the planet initially at 269.8 m/s in the negative x direction and the planet is moving at 31.4 m/s in the positive x direction.  What is the magnitude of the final velocity of the probe, in m/s, after the collision?

bobpursley · Answer

momentum
M*31.3-ME-6*269.8=MV1+ME-6 V2

v1=(31.3-269.8E-6-E-6 V2)

energy
1/2 M*31.2^2+1/2 M E-6 269.8=1/2 MV1^2+1/2 ME-6V2

now put V1 into this, and proceed to solve for V2. A bit of algebra is involved. Notice in the energy equations, M drops out.

Kimmy · Answer

I am just so confused!