Question

A 90-kg halfback running north with a speed of 10 m/s is tackled by a 120-kg opponent running south at 4 m/s. The collision is perfectly inelastic. Compute the velocity of the two players just after the tackle.

a. 0.57 m/s north
b. 2.86 m/s south
c. 2.00 m/s north
d. 1.14 m/s south

Answer 1

In a perfectly inelastic collision, the two objects stick together after the collision and move as one object. To find the velocity of the two players just after the tackle, we can apply the law of conservation of momentum.

Step-by-step explanation:

In a perfectly inelastic collision, the two objects stick together after the collision and move as one object. To find the velocity of the two players just after the tackle, we can apply the law of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.

Let's consider the positive direction as north. The initial momentum is given by p1 = m1 * v1 + m2 * v2, where m1 and v1 are the mass and velocity of the first player, and m2 and v2 are the mass and velocity of the second player. Substituting the given values, we get:

p1 = (90 kg) * (10 m/s) + (120 kg) * (-4 m/s) = 900 kg·m/s - 480 kg·m/s = 420 kg·m/s.

Since the collision is perfectly inelastic, the two players stick together after the tackle. Let's denote the final velocity as vf. The final momentum is given by p2 = (m1 + m2) * vf = 210 kg * vf.

Since the total momentum before the collision is equal to the total momentum after the collision, we have:

420 kg·m/s = 210 kg * vf

Solving for vf, we have vf = 2 m/s.

So, after the tackle, the players have a velocity of 2.00 m/s north.