A 2.5-kg ball and a 5.0-kg ball have an elastic collision. Before the collision, the 2.5-kg ball was at rest and the other ball had a speed of 3.5 m/s. What is the kinetic energy of the 2.5-kg ball after the collision?

In elastic collision, the sum of momentum of the objects before collision will be equal to the sum of momentum of the objects after collision.

We know that momentum is the product of mass and velocity acting on any object.

So, the conservation of energy in elastic collision leads to following equation:

[tex]M_{1} u_{1} +M_{2} u_{2}=M_{1} v_{1}+M_{2} v_{2}[/tex]

Since, the momentum is conserved ,the kinetic energy will also be conserved in elastic collision. So

[tex]M_{1} u_{1} ^{2}+M_{2} u_{2} ^{2}=M_{1}v_{1} ^{2}+ M_{2}v_{2} ^{2}[/tex]

Since initial velocity for M1 ball is zero, then

[tex]M_{2} u_{2}=M_{1} v_{1}+M_{2} v_{2}[/tex]

and

[tex]M_{2} u_{2} ^{2}=M_{1}v_{1} ^{2}+ M_{2}v_{2} ^{2}[/tex]

So, on solving all the above equation, we get an equation for velocity and that is

[tex]\frac{2M_{2}u_{2} }{(M_{1}+M_{2} }[/tex]=final velocity of ball with mass 2.5 kg

[tex]v = \frac{2(5*3.5)}{2.5+5}=4.67 m/s[/tex]

So kinetic energy will be 1/2 mv2

Kinetic energy of 2.5 kg ball is [tex]\frac{1}{2}*2.5*(4.67)^{2} =27.09 J[/tex]

So the kinetic energy of 2.5 kg ball after collision is 27.09 J.