# A ball with a mass of  23 kg is rolling at 25 m/s and elastically collides with a resting ball with a mass of  2 kg. What are the post-collision velocities of the balls?

Feb 8, 2016

${v}_{2 a} = 1 , 038 \frac{m}{\sec}$
${v}_{1 a} = 23 , 962 \frac{m}{\sec}$

#### Explanation:

$\Sigma {P}_{b} = \Sigma {P}_{a}$
$\Sigma {P}_{b} \text{: sum of momentums before}$
$\Sigma {P}_{a} : \text{ sum of momentums after}$
$23 \cdot 25 + 0 = 23 \cdot {v}_{1 a} + 2 \cdot {v}_{2 a}$
$575 = 23 \cdot {v}_{1 a} + 2 \cdot {v}_{2 a}$
${v}_{1 b} + {v}_{2 b} = {v}_{1 a} + {v}_{2 a}$
25+0=v_(1a)+v_(2a) "
${v}_{1 a} = 25 - {v}_{2 a}$
$575 = 23 \left(25 - {v}_{2 a}\right) + 2 \cdot {v}_{2 a}$
$575 = 575 \cdot {v}_{2 a} - 23 \cdot {v}_{2 a} + 2 \cdot {v}_{2 a}$
$554 \cdot {v}_{2 a} = 575$
${v}_{2 a} = 1 , 038 \frac{m}{\sec}$
$25 = {v}_{1 a} + 1 , 038$
${v}_{1 a} = 25 - 1 , 038$
${v}_{1 a} = 23 , 962 \frac{m}{\sec}$