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A 92 -kg fullback, running at$5.0 \mathrm{m} / \mathrm{s},$ attempts to dive directly across the goal line for a touchdown. Just as he reaches the line, he is met head-on in midair by two 75 -kg linebackers, both moving in the direction opposite the fullback. One is moving at $2.0 \mathrm{m} / \mathrm{s}$ and the other at $4.0 \mathrm{m} / \mathrm{s}$ They all become entangled as one mass.a. Sketch the event, identifying the "before" and "after" situations.b. What is the velocity of the football players after the collision?c. Does the fullback score a touchdown?

Fullback will score a touchdown.

Physics 101 Mechanics

Chapter 9

Momentum and Its Conservation

Section 2

Conservation of Momentum

Kinetic Energy

Energy Conservation

Moment, Impulse, and Collisions

University of Michigan - Ann Arbor

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here Weaken job the before picture. And we just have essentially three football players and we'll just label them A, B and C. And we know that A has initial velocity to the right. B has initial velocity to the left as well a c and we can say that if this was the positive X direction after, we simply have a three team, a three person system, football players, A, B and C and we have then some final velocity to the right or to the left tour. Essentially, we would need to figure it out before, um, so I'm just gonna put it to the right for now and we can doesn't be party for Part B. We want to find the velocity of the football players after the collision. So this velocity final, we can say that the initial momentum equals the final momentum. And so we can say that I m sub a visa a initial plus M c b visa be initial plus, um, subsea, the subsea initial Equalling I m. C A plus and be plus M sub sea quantity multiplied by the final velocity. So the final velocity is then going to be equaling two again the some of these impulses divided by the sum of the masses. And so we have 92 kilograms multiplied by 5.0 meters per second. Then we have 75 kilograms multiplied by negative 2.0 meters per second. Given that he is acting in the opposite direction, this will be plus 75 kilograms multiplied by negative four 0.0 meters per second. And we find then rather, this would be, uh, divided first by 92 plus 75 plus 75. Of course, the units, our kilograms. And we find then that the final velocity of the of all three players would be 0.0 for one meters per second. So this is positive. Which means that here this is a vector is in the correct direction. However, it za Satan, this must make it much smaller. And so for part C, does the fullback score a touchdown? We can say yes. The final velocity ah is greater than zero. And, uh, the positive X direction is to the right and based off of the two diagrams again, we can say that Yes, the fullback continues on with the ball and the football eventually crosses the goal line and the fullbacks scores a touchdown. That is the end of the solution. Thank you for watching.

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