## Essential University Physics: Volume 1 (3rd Edition)

$v_2=.693cos30\hat{i}+.693sin30\hat{j}$ $v_3=.693cos30\hat{i}-.693sin30\hat{j}$ $v_1==.386cos30\hat{i}$
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: $v_2=.693cos30\hat{i}+.693sin30\hat{j}$ $v_3=.693cos30\hat{i}-.693sin30\hat{j}$ $v_1=1.386cos(30)\hat{i}-1\hat{i}=.386cos30\hat{i}$