In the "slingshot effect," the transfer of energy in an elastic collision is used to boost the energy of a space probe so that it ca n escape from the solar system. Figure shows a space probe moving at 10.4 km/s (relative to the sun) toward Saturn, which is moving at 9.6 km/s (relative to the sun) toward the probe. Because of the gravitational attraction between Saturn and the probe, the probe swings around Saturn and heads back in the opposite direction with speed v_f. 

(a) Assuming this collision to be a one-dimensional elastic collision with the mass of Saturn much greater than that of the probe, find v_f.

(b) By what factor is the kinetic energy of the probe increased? Where does this energy come from?

Transcribed Image Text:

9.6 km/s 10.4 km/s