M2 collisions help needed!!! Solomon Paper C Question 6

Three uniform spheres A, B and C of equal radius have masses 3m, 2m and 2m respectively. Initially, the spheres are at rest on a smooth horizontal table with their centres in a straight line and with B between A and C. Sphere A is projected directly towards B with speed u. Give that the coefficient of restitution between A and B is (2/3),

a. Show that the speeds of A and B after the collision are (1/3)u and u respectively.

The coefficient of restitution between B and C is e. Given that A and B collide again,

b. Show that e>(1/3)


I solved part a. but i'm unable to solve part b. What do I do here? Please help!!!!

Thank you

You need to work out the velocity of B after the collision with C; this will be in terms of "e".

You're told A and B collide again, and this implies a restriction on the velocity of B, which you need to work out.

Putting the two together should allow you to work out the restriction on "e".