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: 74


$v_2=.693cos30\hat{i}+.693sin30\hat{j}$ $v_3=.693cos30\hat{i}-.693sin30\hat{j}$ $v_1==.386cos30\hat{i}$

Work Step by Step

We know that the angle that the balls will all go at will be 30 degrees. We also know that momentum is conserved. Thus, we know from the fact that the y momentum is conserved that the two balls that are struck will be moving with equal speeds. We also know: $mv_0=mv_f + 2mv{23}$ $v_0=v_f + 2v_{23}cos30^{\circ}$ $v_f=v_0-1.73v_{23}$ We also know from conservation of kinetic energy that: $\frac{1}{2}v_0^2 = \frac{1}{2}v_f^2+ v_{23}^2$ Thus, we find: $\frac{1}{2}v_0^2 = \frac{1}{2}(v_0-1.73v_{23})^2+ v_{23}^2$ $v_{23}=.693v_0$ Thus, we can find the velocities: $v_2=.693cos30\hat{i}+.693sin30\hat{j}$ $v_3=.693cos30\hat{i}-.693sin30\hat{j}$ $v_1=1.386cos(30)\hat{i}-1\hat{i}=.386cos30\hat{i}$
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