Problem 8-34 Elastic collision - Part 6

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

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

$2.733\; v{_2}' = 8.589 \\ v{_2}' = 3.14\; m/s$
 
$v{_1}'$ can be obtained by substituting $v{_2}'$ into $\text{Eqn.#1}$

Do this before continuing.

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