The first ball of mass m moving witha velocity u collides head on with the second ball of mass m at rest.If the coefficient of restitution is e,then what is the ratio of the velocities of the first and the second ball after the collision?

1 Answer
Feb 14, 2018

As no external force is not acting during the collision,we can apply,law of conservation of momentum.

Let,the 1st ball will move with a velocity of vv and the 2nd one with xx after the collision.

so, m u +m*0 = m*v +m*xmu+m0=mv+mx

or, v+x =uv+x=u ...1

Now,coefficient of restitution in this case = (x-v)/(u-0)=exvu0=e (coefficient of restitution is defined as the ratio of relative velocity after the collision to relative veocity before the collision)

o, x-v = euxv=eu .... 2

solving, 1 & 2 we get,

x= (u(e+1))/2x=u(e+1)2 and , v= (u(1-e))/2v=u(1e)2

So, v:x = (1-e):(1+e)v:x=(1e):(1+e)