A ball with a mass of # 2 kg# is rolling at #6 m/s# and elastically collides with a resting ball with a mass of #9 kg#. What are the post-collision velocities of the balls?

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Answer 1 · 2017-09-01T07:13:45

The velocity of the first ball is #=-3.82ms^-1#
The velocity of the second ball is #=2.18ms^-1#

As the collision is elastic, we have conservation of linear momentum and conservation of kinetic energy.

#m_1u_1+m_2u_2=m_1v_1+m_2v_2#

#1/2m_1u_1^2+1/2m_2u_2^2=1/2m_1v_1^2+1/2m_2v_2^2#

so,

#2*6+9*0=2v_1+9v_2#,

#=>#, #v_1=(12-9v_2)/(2)#........................#(1)#

#1/2* 2*6^2+1/2*9*0=1/2*2*v_1^2+1/2*9*v_2^2#

#2v_1^2+9v_2^2=72#..........................#(2)#

Solving for #v_1# and #v_2# from equations #(1)# and #(2)#

#2*((12-9v_2)/(2))^2+9v_2^2=72#

#(12-9v_2)^2+18v_2^2=144#

#144-216v_2+81v_2^2+18v_2^2=144#

#v_2(99v_2-216)=0#

#v_2=0# or #v_2=216/99=2.18ms^-1#

#v_1=1/2(12-9*2.18)=-3.82ms^-1#