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Answer :
Final answer:
The defensive tackle must be moving at a speed of 4.67 m/s before the collision to bring both himself and the running back to a complete stop afterward. This solution utilizes the conservation of momentum principle.
Explanation:
The question involves a scenario where two football players collide and come to rest, highlighting the physics concept of conservation of momentum. In this case, the player's momentum and the defensive tackle's momentum must cancel each other out for both of them to come to a stop post-collision.
To solve for the tackle's speed before the collision, we can use the principle of conservation of momentum:
Momentum before = Momentum after
(mass of running back × speed of running back) + (mass of tackle × speed of tackle) = 0 (since their speed afterward is zero)
(84 kg × 7 m/s) + (126 kg × speed of tackle) = 0
588 kg·m/s + (126 kg × speed of tackle) = 0
Speed of tackle = -588 kg·m/s / 126 kg
Speed of tackle = -4.67 m/s
The negative sign indicates that the tackle is moving in the opposite direction to the running back.
Therefore, the defensive tackle must be moving at a speed of 4.67 m/s before the collision to bring both players to a complete stop post-collision.
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