Three smooth spheres X, Y and Z of masses m, 2m and 3m respectively are arranged in a straight line on a horizontal, friction-free track. Spheres Y and Z are initially at rest. Sphere X approaches Y with speed 10m s−1 and collides with it. Immediately after, Y collides with Z. For every collision the coefficient of restitution is 0.60.
a. (i) Find the speed (magnitude and direction) of X just after its collision with Y.
b. (ii) Find the speed of Y just after its collision with Z.
c. (iii) Find the speed of Z after it is struck by Y.