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 1400 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 60 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

Mass of Car A= 1900 kg

mass of car B =1400 kg

velocity of car b=17 m/s

Car A has a momentum Pa = 1900*Va angle 0

car B has a momentum Pb = 1400*17 angle -90 = 23800 angle -90

R has momentum R = R angle -60

Ax = 1900*Va

Bx = 0

Rx = Rcos(-60)

Ay = 0

By = -23800

Ry = Rsin(-60)

summing x and y

1900*Va = Rcos(-60)

-23800 = Rsin(-60)

from the last, R = 27482

1900*Va = Rcos(-60)

1900*Va = 27482 cos(-60)

Va = 7.23 m/s (b)

total mass is 3300 kg, so if total momentum (R) is 27482 then

Vr = 27482/3300 = 8.32 m/s (a)

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