Two cars collide at an intersection. Car A, with a mass of 2000 kg, is going fro

Question

Two cars collide at an intersection. Car A, with a mass of 2000 kg, is going from west to east, while car B of mass 1300 kg, is going from north to south at 15.0 m/s. As a result of this collision, the two cars become enmeshed and move as one afterwards. In your role as an expert witness, you inspect the scene and determine that, after the collision, the enmeshed cars moved at an angle of 60.0 degree south of east from the point of impact. How fast were the enmeshed cars moving just after the collision? How fast was car A going just before the collision?

Explanation / Answer

before collision

initial momentum Pi = mA*vA + mB*vB

Pi = 2000*vAi - 1300*15j

after collision

final momentum Pf = (mA+mB)*V

Pf = (2000+1300)*(v*cos60i - vsin60 j)

from momentum conservaton Pf = Pi

(2000+1300)*(v*cos60i - vsin60 j) = 2000*vAi - 1300*15j

3300*v*cos60 i - 3300*v*sin60j = 2000*vAi - 1300*15j

comparing j

- 3300*v*sin60 = - 1300*15

v = 6.823 m/s    <<------------answer

comparing i

3300*v*cos60 = 2000*vA

3300*6.823*cos60 = 2000*vA

vA = 5.63 m/s <<<------------answer

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