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What is the velocity of a 900-kg car initially moving at 30.0 m/s, just after it hits a 150-kg deer initially running at 12.0 m/s in the same direction? Assume the deer remains on the car.
Question by OpenStax is licensed under CC BY 4.0.
Final Answer
$27.4\textrm{ m/s}$
Solution Video

OpenStax College Physics Solution, Chapter 8, Problem 26 (Problems & Exercises) (1:43)

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Video Transcript

This is College Physics Answers with Shaun Dychko. A car is moving to the right with a velocity of positive 30.0 meters per second—we are taking the 'right' to be the positive direction— and it's going to collide with a deer that's running in the same direction with a speed of 12.0 meters per second and the car has a mass of 900 kilograms and the deer has a mass of 150 kilograms. After the collision, we assume that the deer sticks to the car so afterwards, there's only one object— it's this deer-car thing— and that is going to be moving with some velocity <i>v prime</i> So we are going to write down our conservation of momentum expression here and so the total momentum initially, <i>P 1</i> plus <i>P 2</i>, that is the momenta before collision, equals the total momentum afterwards and there's only one object so there's only one term here, we'll call it <i>P prime</i>. So <i>P 1</i> is the momentum of the car so that's mass 1 times velocity 1 and then plus the momentum of the deer which is mass 2 times velocity 2 and that's going to equal the total mass of this system here which is <i>m 1</i> plus <i>m 2</i> multiplied by its speed <i>v prime</i>. Our job is to solve for the speed of the car, which is <i>v prime</i>, and so we'll divide both sides here by <i>m 1</i> plus <i>m 2</i> and then switch the sides around as well and we get <i>v prime</i> then is <i>m 1v 1</i> plus <i>m 2v 2</i> over <i>m 1</i> plus <i>m 2</i>. So that's 900 kilograms times 30.0 meters per second plus 150 kilograms times 12.0 meters per second divided by the total mass giving us a speed of 27.4 meters per second and that's a velocity actually—it's positive and it's to the right—and there we go!