Static Equilibrium

Question

Please help me answer the following question, please provide steps, and work.

I know the question is specific, but I did not come up with it. Thanks!

Question:

In the movie, The Matrix Reloaded, Neo (80 kg) jumps toward Agent Smith (600 kg) who jumps towards Neo. When they collide, they grab hold of one another. If Neo has a velocity of 25.0 m/s to the right and Agent Smith has a velocity of 5.0 m/s to the left before the collision, what is the velocity of Agent Smith after the collision?

Make use of the situations in this scenario and tell us a story of your own that involves a similar type of collision. You may use approximate values to solve the problem that you come up with.

Answer 1

Momentum is conserved meaning the momentum before the collision equals the momentum after the collision.

I'll define velocity to the right as positive and to the left as negative.

Momentum (P) is mass (m) multiplied by velocity (v), i.e., P = mv.

The total momentum before the collision is P_Neo + P_Smith = m_Neo•v_Neo + m_Smith•v_Smith = (80)(25) + (600)(-5) = 2000 - 3000 = -1000 kg•m/s

After the collision the velocity of Neo and Smith are the same because they grabbed hold of each other. The mass after the collision is m_Neo + m_Smith = 50 + 600 = 650 kg. The total momentum after the collision is P_Neo-Smith = m_Neo-Smith•v_Neo-Smith = (650)(v)

Since momentum is conserved P_before = P_after or -1000 = 650v so v = -1000/650 = -1.54 m/s or 1.54 m/s to the left

I'll leave it to you to come up with a similar problem. It could be a car and truck head-on collision where the vehicles lock together. It could be two skaters (kid and large adult) that crash and hold on to each other. Or any other of such types of things.