A ball with a mass of # 5 kg# is rolling at #12 m/s# and elastically collides with a resting ball with a mass of #2 kg#. What are the post-collision velocities of the balls?

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Answer 1 · 2018-05-22T09:41:08

The velocities are #=5.14ms^-1# and #=17.14ms^-1#

As the collision is elastic, there is conservation of 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_2^21/2m_1v_1^2+1/2m_2v_2^2#

Threfore,

#5*12+2*0=5v_1+2v_2#

#5v_1+2v_2=60#............................#(1)#

#1/2*5*12^2+1/2*2*0^2=1/2*5v_1^2+1/2*2v_2^2#

#5v_1^2+2v_2^2=720#.........................#(2)#

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

#{(5v_1+2v_2=60),(5v_1^2+2v_2^2=720):}#

#<=>#, #{(v_2=1/2(60-5v_1)),(5v_1^2+2v_2^2=720):}#

#5v_1^2+2*(1/2(60-5v_1))^2=720#

#10v_1^2+3600-600v_1+25v_1^2=1440#

#35v_1^2-600v_1+2160=0#

#v_1=(600+-sqrt((-600)^2-4*35*2160))/(2*35)#

#=(600+-240)/70#

Therefore,

#v_1=12ms^-1# or #v_1=5.14ms^-1#

#v_2=0ms^-1# or #v_2=17.14ms^-1#