A ball with a mass of $5 kg$ is rolling at $18 m/s$ and elastically collides with a resting ball with a mass of $3 kg$ . What are the post-collision velocities of the balls?

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Answer 1 · 2018-05-09T03:57:02

Given

Mass of 1st ball $m_1=5$ kg

Mass of 2nd ball $m_2=3$ kg

Initial velocity of 1st ball $u_1=18m"/"s$

Initial velocity of 2nd ball $u_2=0m"/"s$

Let post collision velocity of 1st ball be $v_1$ and that of 2nd ball be $v_2$

$m_1u_1+m_2u_2=m_1v_1+m_2v_2$

$5*18+3*0=5v_1+3v_2$

$=>5v_1+3v_2=90.....[1]$

Again the collision being elastic one the relative velocity of one ball with respect to the other is reversed by the collision and we get

$v_2-v_1=u_1-u_2$

$=>v_2-v_1=18-0$

$=>v_2-v_1=18.......[2]$

By [1] and [2] we get

$5v_1+3(18+v_1)=90$

$=>8v_1=90-54=36$

$=>v_1=36/8=4.5$ m/s

$v_2=18+v_1=18+4.5=22.5$ m/s

A ball with a mass of 5 kg 5 kg is rolling at 18 m/s18 m/s and elastically collides with a resting ball with a mass of 3 kg3 kg. What are the post-collision velocities of the balls?