16 5. A smooth uniform sphere P has mass 0.3 kg. Another smooth uniform sphere Q, with the same radius as P, has mass 0.2 kg. The spheres are moving on a smooth horizontal surface when they collide obliquely. Immediately before the collision the velocity of P is (4i + 2j) m s–1 and the velocity of Q is (–3i + j) m s–1. At the instant of collision, the line joining the centres of the spheres is parallel to i. The kinetic energy of Q immediately after the collision is half the kinetic energy of Q immediately before the collision. (a) Find (i) the velocity of P immediately after the collision, (ii) the velocity of Q immediately after the collision, (iii) the coefficient of restitution between P and Q, carefully justifying your answers. (11) (b) Find the size of the angle through which the direction of motion of P is deflected by the collision. (3) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________