Two identical balls A and B are approaching each other with velocity $3 m s^{- 1} a n d 7 m s^{- 1}$ respectively and undergo an elastic collision. Determine the velocities of two balls after the collision.

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Solution

Step 1:
Here $m_{1} = m_{2} = m, u_{1} = 3 m s^{- 1}, u_{2} = 7 m s^{- 1} .$
Velocities after the collision are given by
$v_{1} = (\frac{m_{1} - m_{2}}{m_{1} + m_{2}}) u_{1} + \frac{2 m_{2} u_{2}}{(m_{1} + m_{2})}$
$\Rightarrow v_{1} = (\frac{m - m}{m + m}) u_{1} + \frac{2 m u_{2}}{(m + m)}$
$\Rightarrow v_{1} = 0 + u_{2} \Rightarrow v_{1} = u_{2} = - 7 m s^{- 1}$
Step 2:
$v_{2} = (\frac{m_{2} - m_{1}}{m_{1} + m_{2}}) u_{2} + \frac{2 m_{1} u_{1}}{(m_{1} + m_{2})} \Rightarrow v_{2} = (\frac{m - m}{m + m}) u_{2} + \frac{2 m u_{1}}{(m + m)} \Rightarrow v_{2} = 0 + u_{1} \Rightarrow v_{2} = u_{1} = 3 m s^{- 1}$
Thus, bodies will interchange their velocities after the collision.

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