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One 110 kg football lineman is running to the right at 2.55 m/s while another 135 kg lineman is running directly toward him at 2.80 m/s.

What are:

(a) The magnitude and direction of the net momentum of these two athletes?

Answer :

Final answer:

The net momentum of the two football linemen is -97.5 kg·m/s, indicating that the net momentum is in the direction of the second lineman running at 2.80 m/s.

Explanation:

The question is asking to calculate the net momentum of two football linemen running towards each other. Momentum is a vector quantity, meaning it has both magnitude and direction, defined by the product of an object's mass and its velocity.

To find the net momentum, we apply the equation p = mv, where p is the momentum, m is the mass, and v is the velocity. The direction of velocity is important; one lineman is running to the right and the other to the left, so their momenta will have opposite signs. For the lineman running to the right at a velocity of 2.55 m/s with a mass of 110 kg, his momentum is p1 = 110 kg × 2.55 m/s = 280.5 kg·m/s. For the lineman running toward him at 2.80 m/s with a mass of 135 kg, his momentum is p2 = 135 kg × (-2.80 m/s) = -378 kg·m/s, the negative sign indicates the opposite direction.

To find the net momentum, we sum the individual momenta: Net momentum = p1 + p2 = 280.5 kg·m/s - 378 kg·m/s = -97.5 kg·m/s. The negative sign here indicates that the net momentum is in the direction of the second lineman.

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