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.

Name: What is the velocity of a 900-kg car initially moving at 30.0 m/s,… | College Physics Answers
Uploaded: 2020-02-04T23:26:00.000Z
Duration: 103 s
Description: 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.

What is the velocity of a 900-kg car initially moving at 30.0 m/s,… | College Physics Answers

$27.4\textrm{ m/s}$

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 v prime So we are going to write down our conservation of momentum expression here and so the total momentum initially, P 1 plus P 2, 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 P prime. So P 1 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 m 1 plus m 2 multiplied by its speed v prime. Our job is to solve for the speed of the car, which is v prime, and so we'll divide both sides here by m 1 plus m 2 and then switch the sides around as well and we get v prime then is m 1v 1 plus m 2v 2 over m 1 plus m 2. 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!

Comments

coleman12332144· Dec 2, 2023

if the deer is running in the same direction wouldn’t you multiply buy -12 in the equation

ShaunDychko· Dec 4, 2023

Hello, thank you for the question. We've taken the conventional coordinate system where the direction to the right is positive, so the deer's velocity is positive since it's to the right. Hope that helps, Shaun