A ball (initially at rest) falls vertically for 2 s and hits a smooth plane inclined at 30 ° to the horizontal. The coefficient of restitution is 5 8 . The distance along the plane between the first and second impact of the ball is

Step-by-step solution

Let the ball strike the plane at A. We assign a co-ordinate system with origin at A. The velocity of the ball while striking the 30 o plane = gt = 2g m/s. The components of u along and perpendicular to the plane are u sin 30 o and u cos 30 o respectively. After impact, the velocity component u sin 30 o along the plane remains unaffected while the component u cos 30 o perpendicular to the plane becomes e(u cos 30 o ) on rebound. Thus velocity of rebound = e ⁡ . 2 g . 3 2 = 3 eg The acceleration perpendicular to the