An MSU linebacker of mass 112.0 kg sacks a UM quarterback of mass 84.0 kg. Just after they collide, they are momentarily stuck together, and both are moving at a speed of 2.50 m/s.

If the quarterback was at rest just before he was sacked, how fast was the linebacker moving just before the collision? (in m/s)

The linebacker was moving at  

Explanation:

We use conservation of momentum to solve this problem.

The initial momentum of the system of two players is the addition of the two linear momentum of each individual player. Recalling that the liner momentum P is defined as the product of the mass of the object (in our case the mass of each player) times its velocity, and noticing that the quarterback (of mass 84 kg) was at rest before the collision, we can write the initial momentum of the system as:

where the quantity represents the unknown initial velocity of the linebacker  of mass 112 kg.

We can also write the expression for the final linear momentum of the system of two players moving together a a speed of 2.5 m/s:

Since the total momentum is conserved in collisions, we set an equation making the initial momentum equal the final momentum of the system of two players. We then solve for the unknown initial velicity:

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