A ball with a mass of 3 kg is rolling at 1 m/s and elastically collides with a resting ball with a mass of 4 kg. What are the post-collision velocities of the balls?

1 Answer
Mar 9, 2016

v_1^'=-1/7 m/s
v_2^'=6/7m/s

Explanation:

m_1*v_1+m_2v_2=m_1v_1^'+m_2v_2^'" "(1)
"total momentum before collision=total momentum after collision"
1/2*m_1*v_1^2+1/2*m_2*v_2^2=1/2.m_1*v_1'^2+1/2*m_2*v_2'^2

m_1*v_1^2+m_2*v_2^2=m_1*v_1'^2+m_2*v_2'^2" "(2)
"we obtain the equation of (3),if we arrange (1) and (2)"
v_1+v_1^'=v_2+v_2^' " "(3)
3*1+4*0=3*v_1^'+4*v_2^'
3=3*v_1^'+4*v_2^'" "(4)
"use (3)"
1+v_1^'=0+v_2^'
v_2^'=1+v_1^'" "(5)
"use (4)"
3=3*v_1^'+4(1+v_1^')
3=3*v_1^'+4+4v_1^'
-1=7v_1^'" "v_1^'=-1/7 m/s
"use (5)"
v_2^'=1-1/7
v_2^'=6/7m/s