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cybernerd
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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?