Question

a ball collides head on with another identical ball at rest if e is between 0and 1 determine ratio of their final velocities in terms of of coefficient of restitution​

Answer 1

Answer:

(e+1)/(e-1)

Step-by-step explanation:

Let the ball collide with rest identical mass with velocity 'v' and let mass of both of them be 'm'

The initial momentum of the system is mv

Let after collision velocity of one ball be 'v1' in backward direction and of second ball be 'v2' in forward direction

So final momentum of the system is

-mv1+mv2

i.e mv2-mv1

Now since no external force come into play so according to law conservation of momentum

P(inital)=P(final)

So mv=mv2-mv1

i.e v=v2-v1---------(i)

Now coefficient of restitution 'e':

e=speed of separation/speed of approach

So,,

e=v1+v2/v

i.e ev=v1+v2----------(ii)

Now first adding i and ii

We get v2=v(e+1)/2-------(iii)

Then subtracting i from ii

We get v1=v(e-1)/2---------(iv)

So v2/v1=(e+1)/(e-1)-------(Answer)