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

1 Answer
Mar 28, 2016

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

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

Explanation:

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