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?

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Answer 1 · 2017-11-11T06:59:41

The velocities of the balls are $=0ms^-1$ and $=25ms^-1$

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

Let the velocity before collision be $u_1ms^-1$ and $u_2ms^-1$

Let the velocity after collision be $v_1ms^-1$ and $v_2ms^-1$

$m_1u_1+m_2u_2=m_1v_1+m_2v_2$

$1/2m_1u_1^2+1/2m_2u_2^2=1/2m_1v_1^2+1/2m_2v_2^2$

Here, we have

$m_1=m_2=2kg$

$u_1=25ms^-1$

$u_2=0ms^-1$

Therefore,

$v_1+v_2=25$

$v_1^2+v_2^2=25^2=625$

$v_1=25-v_2$

$(25-v_2)^2+v_2^2=625$

$625-50v_2+v^2+v^2=625$

$2v_2^2-50v_2=0$

$2v_2(v_2-25)=0$

$v_2=25$ and $v_1=0$

A ball with a mass of 2 kg 2 kg is rolling at 25 m/s25 m/s and elastically collides with a resting ball with a mass of 2 kg 2 kg. What are the post-collision velocities of the balls?