A 2,090-kg Cadillac and a 810.-kg Volkswagen meet at an intersection. The stopli

Question

A 2,090-kg Cadillac and a 810.-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 go 51.1 (degree) north of east from the point of impact. The Cadillac driver, who keeps a close eye on the speedometer, reports that he was traveling at 30.5 m/s when the accident occurred. How fast was the Volkswagen going just before impact?
V= ------- m/s

Explanation / Answer

we have to write the conservation of momentum.

conservation of momentum in north-south direction(x):   

mvolk*vvolk=(mvolk+mcadl)*vx(cadl+volk)           Eq(1)

conservation of momentum in east-west direction(y):     

mcadl*vcadl=(mvolk+mcadl)vy(cadl+volk)           Eq(2)

we know that:                                                     

vy(cadl+volk)=v(cadl+volk)*sin51.5                  Eq(3)

and                                                                   

vx(cadl+volk)=v(cadl+volk)*cos51.5                 Eq(4)

from Eq(2) we obtain vy(cadl+volk)

from Eq(3) we obtain v(cadl+volk)

from Eq(4) we obtain vx(cadl+volk)

from Eq(1) we obtain vvolk

so we have:                                                              

vvolk=(mcadl/mvolk)*vvolk*cotg51.1= 63.5 m/s

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