Answer to Question #118674 in Math for Felix Coleman

Question

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.

Answer 1

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