AB and CD are two smooth parallel walls. A child rolls a ball along ground from A towards point P find PD so that ball reaches point B after striking the wall CD. Given coefficient of restitution e = 0.5
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This involves the law of reflection for elastic collisions. The angle of incidence equals the angle of reflection. With restitution e=0.5, the vertical velocity component is halved after collision, but the horizontal component remains unchanged. The path can be analyzed using geometry. The ball's trajectory from A to B after bouncing off wall CD must satisfy the reflection condition.
Let the distance from the corner to the impact point on CD be PD = x. Using similar triangles from the reflection, the ratio of distances is determined by the coefficient of restitution. The relationship is given by:
Therefore, PD = 0.5 * AD. Given AD is the distance between the walls, which is constant. For the ball to reach B, PD must be half of the distance from the corner to the line perpendicular from A.
Final Answer: PD = AD / 2