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At the intersection of Texas Avenue and University Drive, a yellow subcompact car with mass 950 kg traveling east on University collides with a red pickup truck with mass 1900 kg that is traveling northon Texas and has run a red light ($\textbf{Fig. E8.41}$). The two vehicles stick together as a result of the collision, and the wreckage slides at 16.0 m/s in the direction 24.0$^\circ$ east of north. Calculate the speed of each vehicle before the collision. The collision occurs during a heavy rainstorm; ignore friction forces between the vehicles and the wet road.

$v_{A 1 x}=\left(\frac{m_{A}+m_{B}}{m_{A}}\right) v_{2 x}=\left(\frac{950 \mathrm{kg}+1900 \mathrm{kg}}{950 \mathrm{kg}}\right)(6.5 \mathrm{m} / \mathrm{s})=19.5 \mathrm{m} / \mathrm{s}$$v_{B 1 y}=\left(\frac{m_{A}+m_{B}}{m_{B}}\right) v_{2 y}=\left(\frac{950 \mathrm{kg}+1900 \mathrm{kg}}{1900 \mathrm{kg}}\right)(14.6 \mathrm{m} / \mathrm{s})=21.9 \mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 8

Momentum, Impulse, and Collisions

Section 3

Momentum Conservation and Collisions

Moment, Impulse, and Collisions

Hope College

University of Winnipeg

McMaster University

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problem. 8.41. We have a collision between a yellow subcompact car and a red pickup truck which will call A and B, respectively. They were initially moving well. The the compact car was initially moving east. Pickup truck was originally moving north and then they collide and stick together and move off at 16 meters per 2nd 24 degrees east of north. And since we're calling this X in this why, it's worth noting that this angle is measured from the positive. Why direction? And so, whereas we'd normally expect to have a co sign for the X component of this, for example, we're actually going to use the sign because it's 90 degrees minus. This is 90 degrees minus this ankle. So we know that the white component for this one is zero initially. Similarly, the X component for this 10 initially, then from this and then being careful with using sign for X and co sign for why we know that or we can readily compute that. The X component of the final velocity is six and 1/2 meters per second, and the white components is 14.6 meters per second And now this is a pretty simple exercise in the conservation of momentum because we know that the initial velocity velocities of either one have a zero. Why or x component? So we take the equation for the X component of the momentum. For example, the contribution from the pickup truck is going to be zero. So we just have the mass of the compact car. Time's what we would like to know about it eggs and this is going to be equal to masses of the cars because they're stuck together times the x component of the final velocity. So the initial speed of the compact car Yeah, and so we can see that sister just at me plus m b divided by name, times the X component of the final velocity, both of them together. And this ends up big 19 and 1/2. You just for a second and pretty much the same story again with white component of momentum. Except now we're learning about. But the truck was originally doing and we need the white component of the final velocity. Some of the masses divided by now the massive truck like final speed loss to be sorry. And then putting the numbers in for this one, we find out that it was going 21 points. Oh, I'm sorry. I should also have noted this the compact subcompact car at a massive 50 kilograms like nine. And the pickup truck has a mess. 1900 killer. Otherwise, it will not be clear where these numbers came from. All right, So that's how you figured out when you have an elastic collision and you know, the initial directions have either one or both of you. You could be told what the final outcome in terms of the velocity waas backwards, Figure out how fast

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