---
title: "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:"
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url: "https://nerd-notes.com/ubq/39211/"
date_modified: "2025-03-11T06:20:46+00:00"
---

# 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 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:

![Diagram](https://nerd-notes.com/wp-content/uploads/2024/06/1-272x300.png)

**Part a)** The speed of the ball just after it first bounces off the plane at \(P_1\). *(3 points)*

**Part b)** The time the ball is in flight between points \(P_1\) and \(P_2\). *(3 points)*

**Part c)** The distance \(L\) along the plane from \(P_1\) to \(P_2\). *(3 points)*

**Part d)** The speed of the ball just before it strikes the plane at \(P_2\). *(3 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/39211/*