2D Glancing Collision Problem

[cybernerd]

Homework Statement

Car two is traveling due North and collides with Car one, which is traveling due west. Car One has a mass of 765kg and after the collision it travels at 70km/h, 57 degrees North of West. Car two has a mass of 1100kg and after the collision it travels at 41km/h, 44 degrees North of West. What is the velocity of each car right before impact?

So

Car One - m1 = 765kg, v1f = 70km/h

Car Two - m2 = 1100kg, v2f = 41km/h

Homework Equations

Pyi = Pyf
Pxi = Pxf
P = mv
SINE LAW

The Attempt at a Solution

So, I started by constructing a vector triangle for each car, and using the sine law to determine the other sides.

CAR ONE TRIANGLE

Where one side is the west (x plane/ P1) momentum and one side is the north (y plane/P2) momentum. The hypotenuse (p12) is the final momentum of car one after the collision.

P12 = mv
=(765kg)(70km/h)
=53550 kgxkm/h

cos = adjacent/hypotenuse
= cos44 = P1/53550
P1 = 38520.64...kgxkm/h

sine = opposite/hypotenuse
=sine44 = P2/53550
P2 = 37198.95...kgxkm/h

CAR TWO TRIANGLE

Much the same as the first triangle, except the hypotenuse of this triangle represents the final momentum of the second car.

P12 = mv
= (1100kg)(41km/h)
45100kgxkm/h

cos57 = P1/45100
P1 = 24563.22...kgxkm/h

sine57 = P2/45100
P2 = 37824.04...kgxkm/h

Okay, up to this point, I'm fairly confident that I'm on the right track. It's right here where I'm getting confused. I know I need to add the vector components, but I'm not entirely certain how.

So...

Pyi = Pyf

Py1 = P2 + P2
=37198.95...kgxkm/h + 37824.04...kg x km/h
= 75022.99...kgxkm/h

Pyf = final momentum of car two
= 45100 kgxkm/h

...They do not match. I have accomplished nothing.
My teacher assures me I am using the correct formula, but clearly, I am using it incorrectly. What am I doing wrong?

 

[LowlyPion]

I would rather see you resolve the final mass*velocity vectors (momentum vectors) into x and y components and then combine the vertical components of each and recognize that those components belonged to the vertically traveling car before the collision and all the horizontal momentum must have come from the horizontally traveling car.

 

[nlightner]

I can see that you have correctly used the Pyi = Pyf equation to determine the final momentum of car two. However, there seems to be an error in your calculation of the final momentum of car one. Instead of adding P2 + P2, you should be adding P1 + P2 to get the final momentum in the y-direction. This would give you a final momentum of 75784.27 kgxkm/h for car one, which is closer to the final momentum of car two (45100 kgxkm/h).

Additionally, in your calculation of the final momentum for car two, you used the value of 53550 kgxkm/h, which is the initial momentum of car one. The final momentum of car two should be the same as the initial momentum of car one, so you should use 53550 kgxkm/h instead of 45100 kgxkm/h.

I would also recommend using consistent units throughout your calculations. In this case, it would be best to use kilometers per hour for velocity and kilograms for mass.

Overall, it seems like you have a good understanding of the concepts and equations involved in this problem. I would suggest double-checking your calculations and units to ensure accuracy.