A ball with a mass of  3 kg is rolling at 11 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 27, 2016

$\text{see to animation}$
${v}_{r} = - \frac{11}{7} \frac{m}{s}$
${v}_{y} = \frac{66}{7} \frac{m}{s}$

Explanation:

${m}_{r} : \text{ mass of the red ball}$
${m}_{y} : \text{ mass of the yellow ball}$
${v}_{r} : \text{ velocity of the red ball after collision}$
${v}_{y} : \text{ velocity of the yellow ball after collision}$
$3 \cdot 11 + 0 = 3 \cdot {v}_{r} + 4 \cdot {v}_{y}$
$33 = 3 \cdot {v}_{r} + 4 \cdot {v}_{y} \text{ (1)}$
$11 + {v}_{r} = 0 + {v}_{y} \text{ (2)}$
${v}_{y} = 11 + {v}_{r} \text{ (3)}$
$\text{insert (3) into (2)}$
$33 = 3 \cdot {v}_{r} + 4 \cdot \left(11 + {v}_{r}\right)$
$33 = 3 \cdot {v}_{r} + 44 + 4 \cdot {v}_{r}$
$33 - 44 = 7 \cdot {v}_{r}$
$- 11 = 7 \cdot {v}_{r}$
${v}_{r} = - \frac{11}{7} \frac{m}{s}$
$\text{use (3):}$
${v}_{y} = 11 - \frac{11}{7}$
${v}_{y} = \frac{66}{7} \frac{m}{s}$