A 2000.-kg Cadillac and a 1000.-kg Volkswagen meet at an intersection. The stopl

Question

A 2000.-kg Cadillac and a 1000.-kg Volkswagen meet at an intersection. The stoplight has just turned green, and the Cadillac, heading north, drives forward into the intersection. The Volkswagen, traveling east, fails to stop. The Volkswagen crashes into the left front fender of the Cadillac; then the cars stick together and slide to a halt. Officer Tom. responding to the accident, sees that the skid marks are directed 55.0 degree north of east from the point of impact. The driver of the Cadillac, who keeps a close eye on the speedometer, reports that he was traveling at 30.0 m/s when the accident occurred. How fast was the Volkswagen going just before the impact?

Explanation / Answer

vC = 30 m/s

Applying momentum conservation for the collision,

2000 vCj + 1000 vV i = (2000 + 1000) v (cos55i + sin55j)

2000 x 30 j + 1000 vV i = 1720.73v i + 2457.46 v j

along j vector,

2000 x 30 = 2457.46 v

v = 24.4 m/s

along vector i,

1000 vV = 1720.73 x 24.4

vV = 42 m/s

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