A ball with a mass of 2 kg is rolling at 3 m/s and elastically collides with a resting ball with a mass of 1 kg. What are the post-collision velocities of the balls?

May 19, 2016

${v}_{1}^{'} = 1 \text{ m/s}$
${v}_{2}^{'} = 4 \text{ } \frac{m}{s}$

Explanation:

$\Sigma {\vec{P}}_{b} = {m}_{1} \cdot {\vec{v}}_{1} + {m}_{2} \cdot {\vec{v}}_{2}$
$\Sigma {\vec{P}}_{b} = 2 \cdot 3 + 1 \cdot 0$
$\Sigma {\vec{P}}_{b} = 6 k g \cdot \frac{m}{s} \text{ Total momentum before collision}$

${v}_{1}^{'} = \frac{2 \cdot \Sigma {P}_{b}}{{m}_{1} + {m}_{2}} - {v}_{1}$

${v}_{1}^{'} = \frac{2 \cdot 6}{2 + 1} - 3$

${v}_{1}^{'} = \frac{12}{3} - 3$

${v}_{1}^{'} = 4 - 3 = 1 \text{ "m/s " velocity of "m_1 " after collision}$

${v}_{2}^{'} = \frac{2 \cdot \Sigma {P}_{b}}{{m}_{1} + {m}_{2}} - {v}_{2}$

${v}_{2}^{'} = \frac{2 \cdot 6}{2 + 1} - 0$

${v}_{2}^{'} = 4 \text{ "m/s" velocity of " m_2 " after collision}$