High School

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One 110 kg football lineman is running to the right at 2.65 m/s, while another 135 kg lineman is running directly toward him at 2.70 m/s.

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

(b) What is their total kinetic energy?

Answer :

Final answer:

The net momentum of the two football linemen is -73 kgm/s to the left, and their total kinetic energy is 1749.9125 J.

Explanation:

To answer the student's schoolwork question, we must analyze each lineman's momentum and then combine them to find the net momentum and their total kinetic energy. Momentum is defined as the product of mass and velocity. So, let's calculate:

  • The momentum of the 110 kg lineman running to the right at 2.65 m/s: momentum = mass imes velocity = 110 kg imes 2.65 m/s = 291.5 kg ext{m/s} to the right.
  • The momentum of the 135 kg lineman running toward him at 2.70 m/s: momentum = mass imes velocity = 135 kg imes -2.70 m/s = -364.5 kg ext{m/s} to the left (the negative sign indicates the opposite direction).

To calculate the net momentum, we add both momenta, keeping in mind that they are in opposite directions:

Net momentum = 291.5 kg ext{m/s} - 364.5 kg ext{m/s} = -73 kg ext{m/s} to the left.

Now to compute the total kinetic energy (KE), which is given by the equation KE = (1/2) imes mass imes velocity2. We do this for both linemen and then add the energies:

  • KE of the 110 kg lineman: KE = (1/2) imes 110 kg imes (2.65 m/s)2 = 769.1375 J
  • KE of the 135 kg lineman: KE = (1/2) imes 135 kg imes (2.70 m/s)2 = 980.775 J

The total kinetic energy of the two athletes is thus 769.1375 J + 980.775 J = 1749.9125 J.

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