Essential University Physics: Volume 1 (3rd Edition)

Published by Pearson
ISBN 10: 0321993721
ISBN 13: 978-0-32199-372-4

Chapter 9 - Exercises and Problems - Page 165: 72


The proof is below.

Work Step by Step

We know from conservation of momentum that, since the masses are equal, the overall velocity in the x and y direction are equal before and after the collision. We know that initially the velocity is only in one direction (which we will define as the x direction). Since the collision isn't head on, this means that the first object has a y-component to its velocity after the collision. This means that the y-components after the collision are equal and opposite. Thus: $vsin\theta=-vcos\phi$ $sin\theta=-cos\phi$ Where $\theta$ is the angle from the x axis of the first object and where $\phi$ is the angle from the x axis of the second object. The only time where this statement is true is if theta and phi are both 45 degrees, meaning that the two velocity vectors are perpendicular.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.