# A ball with a mass of  2 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?

Nov 11, 2017

The velocities of the balls are $= 0 m {s}^{-} 1$ and $= 25 m {s}^{-} 1$

#### Explanation:

As the collision is elastic, there is conservation of linear momentum and conservation of kinetic energy

Let the velocity before collision be ${u}_{1} m {s}^{-} 1$ and ${u}_{2} m {s}^{-} 1$

Let the velocity after collision be ${v}_{1} m {s}^{-} 1$ and ${v}_{2} m {s}^{-} 1$

${m}_{1} {u}_{1} + {m}_{2} {u}_{2} = {m}_{1} {v}_{1} + {m}_{2} {v}_{2}$

$\frac{1}{2} {m}_{1} {u}_{1}^{2} + \frac{1}{2} {m}_{2} {u}_{2}^{2} = \frac{1}{2} {m}_{1} {v}_{1}^{2} + \frac{1}{2} {m}_{2} {v}_{2}^{2}$

Here, we have

${m}_{1} = {m}_{2} = 2 k g$

${u}_{1} = 25 m {s}^{-} 1$

${u}_{2} = 0 m {s}^{-} 1$

Therefore,

${v}_{1} + {v}_{2} = 25$

${v}_{1}^{2} + {v}_{2}^{2} = {25}^{2} = 625$

${v}_{1} = 25 - {v}_{2}$

${\left(25 - {v}_{2}\right)}^{2} + {v}_{2}^{2} = 625$

$625 - 50 {v}_{2} + {v}^{2} + {v}^{2} = 625$

$2 {v}_{2}^{2} - 50 {v}_{2} = 0$

$2 {v}_{2} \left({v}_{2} - 25\right) = 0$

${v}_{2} = 25$ and ${v}_{1} = 0$