A ball falls onto an inclined plane of inclination from a height h above the point of impact and undergoes a perfectly elastic collision. At what distance along the incline will it strike the plane again?

Step-by-step solution

Velocity of the ball just before impact is v = 2gh vertically downwards. Taking the x-axis along the inclined plane downwards and the y-axis perpendicular to the plane upwards. The components of velocity just before impact are: v_ x = v v_ y = -v Since the collision is perfectly elastic, the velocity component perpendicular to the plane is reversed, while the parallel component remains unchanged. The velocity components just after impact are: u_ x = v u_ y = v The components of acceleration due to gravity are: a_ x