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Problem 5 Easy Difficulty

One $110-\mathrm{kg}$ football lineman is running to the right at 2.75 $\mathrm{m} / \mathrm{s}$
while another $125-\mathrm{kg}$ lineman is running directly toward him at 2.60 $\mathrm{m} / \mathrm{s}$ . What are (a) the magnitude and direction of the net momentinm of these two athletes, and (b) their total kinetic energy?


(a) $-22.5 \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$
(b) $838 \mathrm{J}$


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Video Transcript

in this question. One athlete with a mass off 110 kg is running to the right with velocity off 2.75 m per second and at the same time another athlete with a mass off 125 kg is moving to the left with velocity off 2.60 m per second in the first item. Off this question, we have to evaluate the net momentum in this situation. The net momentum is nothing else than the sum off. The momentum's so peanut is because two p one plus p Chew And then, by looking at this equation, you see that the momentum is just the product off the mass times the velocity. So P one is equal to the mass off the athlete number one, which is 110 kg times his velocity off 2.75 m per second. Note that I'm adopting the following reference frame, so everything that's points to the right is positive and everything that points the left is negative. The reform velocity off the athlete number two is negative, so it's momentum will be negative. Then we have 125 times, 2.60 and then you get a net momentum off minus 22.5 kg times meters per second. So the magnitude of the net momentum is 22.5 and it has a minus sign in front off it, indicating that its direction is to the left. So the net momentum is 22.5 to the left. Now, in the second item, we have to calculate what is the total kinetic energy in this situation. The total kinetic energy is nothing else than the sum off the kinetic energies and the kinetic energy. By looking at these expression is given by the mass times the velocity squared, divided by two. So we have the mass off the athlete number one, which is 110 times his velocity to 1100.75 squared, divided by two plus magnetic energy. Off added number two, which is 125 kg times his velocity squared, noticed that since well square the velocity. We don't have to worry about that minus sign off the velocity because it's pointing to the left. It will be squared anyway. So the velocity off the second athlete is 2.60 squared, divided by true and these results in the kinetic energy off approximately 838 jewels. And this is the answer to the second item off this question.