A ball of mass $m$ is released from rest at a distance $h$ above a frictionless plane inclined at an angle of $45^\circ$ to the horizontal as shown above. The ball bounces horizontally off the plane at point $P_1$ with the same speed with which it struck the plane and strikes the plane again at point $P_2$. In terms of $g$ and $h$, determine each of the following quantities:

Question

A ball of mass $m$ is released from rest at a distance $h$ above a frictionless plane inclined at an angle of $45^\circ$ to the horizontal as shown above. The ball bounces horizontally off the plane at point $P_1$ with the same speed with which it struck the plane and strikes the plane again at point $P_2$. In terms of $g$ and $h$, determine each of the following quantities:(a) The speed of the ball just after it first bounces off the plane at $P_1$.
, (b) The time the ball is in flight between points $P_1$ and $P_2$.
, (c) The distance $L$ along the plane from $P_1$ to $P_2$.
, (d) The speed of the ball just before it strikes the plane at $P_2$.
:

Rita · Accepted Answer

$ \sqrt{2gh} $
$ \frac{2\sqrt{2gh}}{g} $
$ 4\sqrt{2}h $
$ \sqrt{10gh} $

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