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1. Two small smooth spheres, A and B, of equal radii have masses 3m 10 kg and m 5 kg respectively, where m is a positive constant. They are moving on a smooth horizontal surface with speeds 3u ms−1 and 2u ms−1 respectively, for some u > 0, moving towards each other when they collide. The coefficient of restitution between the two balls is 0.8. (a) Find the speeds of A and B immediately after the collision. (b) Show that the velocity of the center of mass before and after collision are the same. 2. A particle P moving with a constant velocity i+j+k passes through a point with position vector 3i−7j−4k at the same instant as a particle Q passes through a point with position vector −i + j + λk. Q has a constant velocity vector 2i − j − 5k. (a) Find the velocity of Q relative to P. (b) Find the value of λ if P and Q collide. (c) If λ = − 1 2 , find the shortest distance between P and Q.
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