Problem 8-34 Elastic collision - Part 2 - A

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

$m_1\; v_1 = m_1\; v{_1}'+ m_2\; v{_2}'$

Correct!
 
Let's put in the numbers we know:
$(22)(3.5) = (22) v{_1}' + (27) v{_2}' \\ 3.5 = v{_1}' + 1.227\; v{_2}' \;   \text{Eqn. #1}$

Note: In problems like this we can use mixed units that would be improper elsewhere. We have used gm for mass and m/s for velocity. It was not necessary to convert $gm$ to $kg$ as that would only introduce the same multiplying factor on both sides of the equation.

This collision is 'elastic', that means:

(A)  Maximum $E_K$ is lost in the collision.

(B)  Some $E_K$ is lost in the collision.

(C) $E_K$ is conserved.