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*Three balls A, B* and *Cofmasses 2 kg*,4kg and *8 kg*, *respectively*, *move along* the same *straight line* and in the same direction, with velocities 4 m/s, 1 m/s and 3/4 m/sec. If A collides with B and subsequently B collides with C. Find the velocity of ball A and ball B after collision, taking the coefficient of restitution as unity.

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case 1

consider the collision of A and B. Let v and v' be the velocities after collision

by momentum conservation

2v+4v'=12 or v+v'=6...............(1)

relative velocity after impact = -e (relative velocity before impact)

v-v'=-1(4-1) or v-v' =-3 ...................(2)

solving (1) and (2)

v'=3 m/s and v= 0

hence after collision A is at rest and B moves with 3m/sec

now consider the collision of B and C

let v and v' be the new velocities after collision in this case.

from momentum conservation and applying the condition

relative velocity after impact = -e (relative velocity before impact)

let v and v' be the new velocities after collision in this case

we can find that

v=0 and v'=9/4

there for VA=VB=0

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