Problem 8-34 Elastic collision - Part 7

A superball of mass $22\; g$ rolls with a speed of $3.5\; m/s$ toward another (stationary) superball of mass $27\; g$. If the balls have a head-on elastic collision, what are the velocities magnitudes and directions) of the balls after the collision?
[Ans. $3.1\; m/s$ forward and $0.4\; m/s$ backward]

Accumulated Solution

$m_1\; v_1 = m_1\; v{_1}'+ m_2\; v{_2}' \\ 3.5 = v{_1}' + 1.227\; v{_2}' \; \text{Eqn. #1}\\ m_1\; v{_1}{^2} = m_1\; v{_1}'{^2} + m_2\; v{_2}'{^2} \\ 3.5^2 = v{_1}'{^2} + 1.227\;v{_2}'{^2}\; \text{Eqn. #2} \\ v{_2}' = 3.14\; m/s$

$v{_1}' = 3.5 - 1.227\; v{_2}' = 3.5 - 1.227(3.14) = 3.5 - 3.852 \\ v{_1}' = -0.35\; m/s$

 
 So we see that $m_1$ does bounce off of $m_2$ and reverse direction, but we did not have to guess that in advance.

You have completed this problem.