Car A was at rest 27.8 ft south of the point O when it was struck in

Question:

Car A was at rest 27.8 ft south of the point O when it was struck in the rear by car B, which was traveling north at a speed vB. Car C, which was traveling west at a speed vC, was 120 ft east of point O at the time of the collision. Cars A and B stuck together and, because the pavement was covered with ice, they slid into the intersection and were struck by car C which had not changed its speed. Measurements based on a photograph taken from a traffic helicopter shortly after the second collision indicated that the positions of the cars, expressed in feet, were rA = ??30.3i + 50.7j, rB = ??30.3i + 61.2j, and rC = ??59.4i ?? 45.6j. Knowing that the weights of cars A, B, and C are, respectively, 2800 lb, 3600 lb, and 3200 lb, solve the problems indicated. Knowing that vC = 45 mi/h, determine the initial speed of car B and the time elapsed between the first collision and the time the photograph was taken.