10 3. [In this question, i and j are perpendicular unit vectors in a horizontal plane.] A smooth uniform sphere P has mass 0.3 kg. Another smooth uniform sphere Q, with the same radius as P, has mass 0.5 kg. The spheres are moving on a smooth horizontal surface when they collide obliquely. Immediately before the collision the velocity of P is (ui + 2j) m s−1 , where u is a positive constant, and the velocity of Q is (−4i + 3j) m s−1 At the instant when the spheres collide, the line joining their centres is parallel to i. The coefficient of restitution between P and Q is 3 5 As a result of the collision, the direction of motion of P is deflected through an angle of 90° and the direction of motion of Q is deflected through an angle of α° (a) Find the value of u (8) (b) Find the value of α (5) (c) State how you have used the fact that P and Q have equal radii. (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________