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?

1 Answer
May 9, 2018

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#

By conservation of momentum

#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