One object is at rest, and another is moving. The two collide in a one-dimension

Question

One object is at rest, and another is moving. The two collide in a one-dimensional, completely inelastic collision. In other words, they stick together after the collision and move off with a common velocity. Momentum is conserved. The speed of the object that is moving initially is 24 m/s. The masses of the two objects are 3.9 and 8.5 kg. Determine the final speed of the two-object system after the collision for the case (a) when the large-mass object is the one moving initially and the case (b) when the small-mass object is the one moving initially.
(a) vf = ---Select---m/sm/s^2kg

Explanation / Answer

Total momentum before collsion = total momentum after collision

a)
Case 1
Total momentum before collision = 8.5 * 24 = 204 kgm/s

Since the two masses stick together, the mass after collision = 8.5 + 3.9 = 12.4 kg

Total momentum after collision = 12.4 v

So

204 = 12.4 v
v = 204 / 12.4 = 16.45 m/s

b)
Case 2
Total momentum before collision = 3.9 * 24 = 93.6 kgm/s

Total momentum after collision = 12.4 v

93.6= 12.4 v

v = 93.6/12.4 = 7.54 m/s

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