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Question:

Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. These have masses m, 2m, and m, respectively. The object A moves towards B with a speed 9 m/s and makes an elastic collision with it. Thereafter, B makes a completely inelastic collision with C. All motions occur on the same straight line. Find the final speed (in m/s) of the object C.

Solution:

After 1st collision
mvA = mv'A + 2mv'B
0 = v'B - v'A
0 = v'B - v'A
v'B - v'A = -(vA - vB) = v'B - 0 = 9 - v'A
Also, v'B - v'A = -(0 - 9) = 9
Solving these equations,
v'A = 3 m/s
v'B = 6 m/s
After the 2nd collision
2mv'B = (2m + m)vC
2v'B = 3vC
vC = (2/3)v'B
vC = (2/3)(6 m/s)
vC = 4 m/s