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Two football players collide head-on in midair while trying to catch a thrown football. The first player is 95.0 kg and has an initial velocity of 6.00 m/s, while the second player is 115 kg and has an initial velocity of –3.50 m/s. What is their velocity just after impact if they cling together?
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Final Answer

$0.798 \textrm{ m/s}$

Solution Video

OpenStax College Physics Solution, Chapter 8, Problem 41 (Problems & Exercises) (1:29)

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Video Transcript

This is College Physics Answers with Shaun Dychko. We have one football player of mass 95 kilograms moving to the right with a velocity of six meters per second. They're going to collide with another football player moving to the left with a velocity of 3.5 meters per second. Football player number two has a mass of 115 kilograms. This picture is before the collision. After their collision they stick together and the question is what velocity will they have after they stick together after colliding in mid-air. So the total momentum that they have initially before collision which is <i>m one v one</i> plus <i>m two v two</i> has to equal the total momentum that they have after the collision. So there will be a single combined objective mass <i>m one</i> plus <i>m two</i> moving with a single velocity <i>v prime</i>. So we need to solve for <i>v prime</i>. We'll do that by dividing both sides by <i>m one</i> plus <i>m two</i> and then switch the sides around to solve for the unknown on the left. We have <i>v prime</i> equals <i>m one v one</i> plus <i>m two v two</i> divided by the total mass. So we have 95 kilograms times six meters per second for football player one, their initial momentum, plus the momentum initially of the second football player, which is 115 kilograms times negative 3.5 meters per second and I'll divide all that by 95 plus 115, and you get 0.798 meters per second. That's positive which means they will be moving to the right after they stick together.