A ball with a mass of # 2 kg# is rolling at #25 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 · 2017-11-11T06:59:41

The velocities of the balls are #=0ms^-1# and #=25ms^-1#

As the collision is elastic, there is conservation of linear momentum and conservation of kinetic energy

Let the velocity before collision be #u_1ms^-1# and #u_2ms^-1#

Let the velocity after collision be #v_1ms^-1# and #v_2ms^-1#

#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#

Here, we have

#m_1=m_2=2kg#

#u_1=25ms^-1#

#u_2=0ms^-1#

Therefore,

#v_1+v_2=25#

#v_1^2+v_2^2=25^2=625#

#v_1=25-v_2#

#(25-v_2)^2+v_2^2=625#

#625-50v_2+v^2+v^2=625#

#2v_2^2-50v_2=0#

#2v_2(v_2-25)=0#

#v_2=25# and #v_1=0#