Two cars collide at an intersection. Car A , with a mass of 1900 kg , is going f

Question

Two cars collide at an intersection. Car A, with a mass of 1900 kg , is going from west to east, while car B , of mass 1300 kg , is going from north to south at 17 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 65 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

here

add the momentum vectors.

A has a momentum Pa = 1900*Va angle 0
B has a momentum Pb = 1300*17 angle -90 = 22100 angle -90
R has momentum R = R angle -65

Ax = 1900*Va
Bx = 0
Rx = Rcos(-65)
Ay = 0
By = -22100
Ry = Rsin(-65)

summing x and y
1900*Va = Rcos(-65)
-22100 = Rsin(-65)

from the last, R = 24384.65
1900 * Va = Rcos(-65)
1900*Va = 24384.65 * cos(-65)
Va = 5.42 m/s (b)

total mass is 3200 kg, so if total momentum (R) is 24384.65, them
Vr = 24384.65 /3200 = 7.62 m/s (a)

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