A 90-kg halfback running north with a speed of 10 m/s is tackled by a 120-kg opponent running south at 5.0 m/s. The collision is perfectly inelastic. Compute the velocity of the two players just after the tackle.Select one:a.1.4 m/s southb.2.8 m/s southc.1.4 m/s northd.2.8 m/s north
Question
A 90-kg halfback running north with a speed of 10 m/s is tackled by a 120-kg opponent running south at 5.0 m/s. The collision is perfectly inelastic. Compute the velocity of the two players just after the tackle.Select one:a.1.4 m/s southb.2.8 m/s southc.1.4 m/s northd.2.8 m/s north
Solution
To solve this problem, we need to use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.
Step 1: Calculate the initial momentum of both players.
The momentum (p) of an object is calculated by multiplying its mass (m) by its velocity (v). So, for the halfback, p = mv = 90 kg * 10 m/s = 900 kgm/s north. For the opponent, p = mv = 120 kg * 5.0 m/s = 600 kgm/s south.
Step 2: Since they are running in opposite directions, we can consider one of the directions as negative. Let's consider the south direction as negative. So, the total initial momentum is 900 kgm/s - 600 kgm/s = 300 kg*m/s.
Step 3: After the collision, the two players move together (because the collision is perfectly inelastic), so their total mass is 90 kg + 120 kg = 210 kg.
Step 4: The final velocity (v) of the two players can be found by dividing the total momentum by the total mass. So, v = total momentum / total mass = 300 kg*m/s / 210 kg = 1.4 m/s.
Step 5: Since we took the south direction as negative and the result is positive, the direction is north. So, the velocity of the two players just after the tackle is 1.4 m/s north.
So, the correct answer is c. 1.4 m/s north.
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