A ball with a mass of # 5 kg# is rolling at #9 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 · 2017-04-08T09:16:19

The velocity of the first ball is #=3.86ms^-1#
The velocity of the second ball is #=12.86ms^-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#

#m_1=5kg#

#m_2=2kg#

#u_1=9ms^-1#

#u_2=0ms^-1#

Therefore,

#v_1=3/7*9+4/7*(0)=27/7=3.86ms^-1#

#v_2=10/7*9-3/7*(0)=90/7=12.86ms^-1#

Verificaition

#m_1u_1+m_2u_2=5*9+2*0=45#

#m_1v_1+m_2v_2=5*3.86+2*12.86=45#