A ball with a mass of $6 k g$ $6 kg$ is rolling at $6 \frac{m}{s}$ $6 m/s$ and elastically collides with a resting ball with a mass of $8 k g$ $8 kg$ . What are the post-collision velocities of the balls?

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Answer 1 · 2016-03-28T21:23:52

$v_1^'=-6/7 " "m/s$

$v_2^'=36/7 " "m/s$

$m_1*v_1+m_2*v_2=m_1*v_1^'+m_2*v_2^'$
$6*6+8*0=6*v_1^' + 8*v_2^'$
$36+0=6*v_1^'+8*v_2^'$
$36=6*v_1^'+8*v_2^'" "(1)$

$" we use the equation " v_1+v_1^'=v_2+v_2^'$
$" for calculating velocities after collision"$

$6+v_1^'=0+v_2^'$
$6+v_1^'=v_2^'" "(2)$

$36=6*v_1^'+8(6+v_1^')$
$36=6*v_1^'+48+8*v_1^'$
$36-48=14*v_1^'$
$-12=14*v_1^'$
$v_1^'=-12/14=-6/7 " "m/s$

$"use (2)"$
$6-6/7=v_2^'$
$(42-6)/7=v_2^'$

$v_2^'=36/7" " m/s$

A ball with a mass of 6 kg6kg 6 kg is rolling at 6 m/s6ms6 m/s and elastically collides with a resting ball with a mass of 8 kg8kg 8 kg. What are the post-collision velocities of the balls?