23 Turn over Question 6 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 6 is 11 marks) 24 7. v m s–1 1 2 α α A C D B Figure 2 Figure 2 represents the plan view of part of a horizontal floor, where AB and CD represent fixed vertical walls, with AB parallel to CD. A small ball is projected along the floor towards wall AB. Immediately before hitting wall AB, the ball is moving with speed v m s–1 at an angle α to AB, where 0 < α < 2 π The ball hits wall AB and then hits wall CD. After the impact with wall CD, the ball is moving at angle  1 2 α to CD. The coefficient of restitution between the ball and wall AB is  2 3 The coefficient of restitution between the ball and wall CD is also 2 3 The floor and the walls are modelled as being smooth. The ball is modelled as a particle. (a) Show that tan  1 2 α       = 1 3 (7) (b) Find the percentage of the initial kinetic energy of the ball that is lost as a result of the two impacts. (4) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________