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