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 25 m/s. The masses of the two objects are 3.0 and 8.0 kg. Determine the final speed of the two-object system after the collision for the case when the large-mass object is the one moving initially and the case when the small-mass object is the one moving initially.

Large object moving, small object at rest:

v = 18.18m/s

Small object moving, large object rest:

v= 6.81m/s

Explanation:

p = mv

m1•Vi1 + m2•Vi2 = m1•Vf1 + m2•Vf2

First Scenario (large object moving):

For small object,

p=mv

p= 3kg • 0 = 0

For large object,

p= mv

p= 8kg • 25m/s = 200kg•m/s

Combined,

p1+p2 (small object + large object) = 200m/s

After the collision, there is one mass,

new mass is 8kg + 3kg = 11kg

So now , p = mv again. In this case

200m/s = (11kg)•v

v = (200kg•m/s)/(11kg) = 18.18 m/s

Second Scenario (small object moving):

p1v1 = 3kg•25m/s = 75kg•m/s

p2v2 = 8kg•0 = 0

p1v1 + p2v2 = 75kg•m/s

New mass = 8kg+ 3kg = 11kg

p = mv

75kg•m/s = 11kg•v

v = (75kg•m/s)/11kg = 6.81m/s