Two football players are on a collision course! A 93 kg running back is headed straight for a 96 kg linebacker at a rate of 5.3 m/s to the right (+). If the linebacker is moving toward the running back at 2.6 m/s to the left (-), what is the total momentum of the two-player system?

Question

01-04-2025
Physics

High School

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Two football players are on a collision course! A 93 kg running back is headed straight for a 96 kg linebacker at a rate of 5.3 m/s to the right (+). If the linebacker is moving toward the running back at 2.6 m/s to the left (-), what is the total momentum of the two-player system?

Answer :

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AsherIsaiah AsherIsaiah · Answer 1 · 2024-05-29T05:13:56-04:00

Final answer:

The total momentum of the two-football player system before collision is 243.3 kg·m/s to the right, calculated by individually determining the momentum of each player and then adding them together.

Explanation:

To calculate the total momentum of the two-player system before they collide, we need to remember that momentum is a vector quantity, meaning it has both magnitude and direction. Momentum can be calculated using the formula:

p = m × v where p is momentum, m is mass, and v is velocity.

For the 93 kg running back moving at 5.3 m/s to the right, the momentum will be:

p₁ = 93 kg × 5.3 m/s = 492.9 kg·m/s (to the right)

For the 96 kg linebacker moving at 2.6 m/s to the left, the momentum will be:

p₂ = 96 kg × (-2.6 m/s) = -249.6 kg·m/s (to the left, hence the negative sign)

The total momentum of the system is the sum of the momenta:

Total momentum p₁ + p₂ = 492.9 kg·m/s + (-249.6 kg·m/s) = 243.3 kg·m/s (to the right)

Therefore, the total momentum of the two-player system just before the collision is 243.3 kg·m/s to the right.