A 1100 kg car is traveling north at 12 m/s . It approaches an intersection, wher

Question

A 1100 kg car is traveling north at 12 m/s. It approaches an intersection, where a second 2000 kg truck is traveling east with a velocity of 10 m/s. All occupants of the vehicles are wearing seat belts and luckily there were no injuries, but they collide in the intersection. The car and truck stick together in the collision and move away from the collision point as a single object. Find the angle that the velocity of the combined system makes with the initial directions of the vehicles.
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Explanation / Answer

apply conservation momentum alonf North

m1*u1+m2*u2 = -(m1+m2)*V*sin(theta)
(1100*12)+(0) = -(1100+2000)*V*sin(theta)

V*sin(theta) = -4.25

along East
m1*u1+m2*u2 = (m1+m2)*V*cos(theta)
0+(2000*10) = (1100+2000)*V*cos(theta)
V*cos(theta) = 6.45

tan theta = (-4.25/6.45)

theta = -33.38 degrees

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