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 21 m/s. The masses of the two objects are 2.4 and 9.0 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.

Explanation / Answer

This is the case of Momentum conservation

Following formula is apllied in both the cases

m1v1 + Mv2 = (M+m)V

where m =mass of small object       M = mass of the large object

v1 = initial velocity of smaller object       v2 =initial velocity of the larger object

V = Final velocity of the combined massess

a) for the first case when the large object is moving initially

0 + 9*21 = (9+2.4)*V

V = (9*21)/(11.4)

V = 16.58m/s

b) when the smaller object is moving with the initial velocity

2.4*21 + 0 = (9+2.4)*V

V = 2.4*21 / 11.4

V = 4.42m/s

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