A ball with a mass of # 3 kg# is rolling at #5 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 · 2017-05-07T09:25:17

The velocity of the first ball is #=-2.5ms^-1#
The velocity of the second ball is #=2.5ms^-1#

In an elastic collision, we have conservation of momentum and conservation of kinetic energy

#m_1u_1+m_2u_2=m_1v_1+m_2v_2#

and

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

Solving the above 2 equations for #v_1# and #v_2#, we get

#v_1=(m_1-m_2)/(m_1+m_2)*u_1+(2m_2)/(m_1+m_2)*u_2#

and

#v_2=(2m_1)/(m_1+m_2)*u_1+(m_2-m_1)/(m_1+m_2)*u_2#

Taking the direction as positive #rarr^+#

#m_1=3kg#

#m_2=9kg#

#u_1=5ms^-1#

#u_2=0ms^-1#

Therefore,

#v_1=-6/12*5+18/12*(0)=27/7=-2.5ms^-1#

#v_2=6/12*5-6/12*(0)=90/7=2.5ms^-1#

Verificaition

#m_1u_1+m_2u_2=3*5+9*0=15#

#m_1v_1+m_2v_2=-3*2.5+9*2.5=6*2.5=15#