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?
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Please see the first Related Question below.
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