Turn over 15 Question 4 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 4 is 8 marks) 16 5. v m s−1 A B C θ Figure 1 Figure 1 represents the plan view of part of a horizontal floor, where AB and BC represent fixed vertical walls, with AB perpendicular to BC. A small ball is projected along the floor towards the wall AB. Immediately before hitting the wall AB the ball is moving with speed v m s−1 at an angle θ to AB. The ball hits the wall AB and then hits the wall BC. The coefficient of restitution between the ball and the wall AB is 1 3 The coefficient of restitution between the ball and the wall BC is e. The floor and the walls are modelled as being smooth. The ball is modelled as a particle. The ball loses half of its kinetic energy in the impact with the wall AB. (a) Find the exact value of cos θ. (5) The ball loses half of its remaining kinetic energy in the impact with the wall BC. (b) Find the exact value of e. (5) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________