How Do You Calculate Velocities in a Three-Ball Elastic Collision?

[Emily-x]

Homework Statement

The first ball (A), of mass 0.5 Kg is rolled towards the second (B) at a velocity of 3.5 ms. Ball B then impacts ball C.

Assume this collision is perfectly elastic.

Calculate:
a. The velocity at which ball A recoils after impacting with ball B.
b. The velocity with which ball B collides with ball C
c. The velocity with which ball B recoils from ball C
d. The velocity at which ball C is moving after ball B has collided with i

I don't know how to work this out! :/

 

[mrkrgn]

is there friction? as in is it actually rolling or sliding?

 

[Emily-x]

Mass;

Ball A = 0.5 kg
Ball B = 0.782 kg
Ball C = 0.386 kg

No friction just that ball A is moving at 3.5ms on a flat surface

 

[mrkrgn]

do the collision between a and b first. total momentum before the impact equals the total momentum after, and the relative velocity after impact equals (-e)time relative velocity before impact. call initial velocities u1 and u2 and after collision v1 and v2

so,
m1u1+ m2u2 = m1v1 + m2v2

and

v2-v1 = -e(u2-u1)

you know u1 and u2 as 3.5 and 0 and you also know m1 and m2 as 0.5 and 0.782

just plug in the values and solve simultaneously

 

[Emily-x]

Thanks, I'll try.. I've never done Physics before!

 

[Emily-x]

The velocity at which ball A recoils after impacting with ball B

-0.7698907956318254

The velocity at which ball B collides with ball C

2.7301092043681745

The velocity at which ball B recoils from ball C

0.9256192165494838

The velocity at which ball C is moving after ball B has collided with it

3.6557284209176584