A girl is traveling North when she enters an intersection. When she reaches the

Question

A girl is traveling North when she enters an intersection. When she reaches the center of the intersection, her car is struck by another car which is traveling East. The two cars remain joined together after the collision and skid to a stop. You determine that after the collision the cars skidded 20 m at an angle of 30 degrees north of east before stopping. You determine that the weight of her car was 800 kg and that of the other car was 1400 kg, where you included the driver's weight in each case. The coefficient of kinetic friction for a rubber tire skidding on dry pavement is 0.85. What is the speed of each car prior to the collision?

Explanation / Answer

From work energy theorem

   W = K

    mg*x = 1/2mv^2

then the speed

   v = 2gx = 2(0.85)(9.8)(20)

                   = 18.25 m/s

Now from law of conservation of momentum

along east

     1400 v2 = (800 + 1400)(18.25) cos30

then the speed of the another car

        v2 = (2200)(15.8) /1400

             = 24.84 m/s

along North

      800v1 = (800 + 1400) (18.25)sin30

then the speed of the girl car

    v1 = (2200)(9.125) /800

        = 25m/s

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