A ball with a mass of  3 kg is rolling at 15 m/s and elastically collides with a resting ball with a mass of 4 kg. What are the post-collision velocities of the balls?

Feb 15, 2016

${v}_{1} = - \frac{15}{7} \frac{m}{2}$
${v}_{2} = \frac{90}{7}$m/s

Explanation:

$\text{we must use conservation of momentum to solve this problem.}$
${\vec{P}}_{1} + {\vec{P}}_{2} = {\vec{P}}_{1}^{'} + {\vec{P}}_{2}^{'}$
$3 \cdot 15 + 0 = 3 \cdot {v}_{1} + 4 \cdot {v}_{2}$
$15 + {v}_{1} = 0 + {v}_{2}$
${v}_{1} = {v}_{2} - 15$
$3.15 = 3 \left({v}_{2} - 15\right) + 4 \cdot {v}_{2}$
$45 = 3 \cdot {v}_{2} - 45 + 4 \cdot {v}_{2}$
$90 = 7 \cdot {v}_{2}$
${v}_{2} = \frac{90}{7}$m/s
${v}_{1} = \frac{90}{7} - 15$
${v}_{1} = - \frac{15}{7} \frac{m}{2}$