A car weighing 3572 lbs is heading east and collides with a van weighing 4123 lb

Question

A car weighing 3572 lbs is heading east and collides with a van weighing 4123 lbs heading north. After the collision, the car moves off at angle of 37.5° north of east and skids a distance of 40.34 ft before it comes to rest. The van moves off at an angle of 66.5° north of east and skids 13.78 ft before coming to rest. You can assume that the brakes are applied immediately following the collision, that the brakes lock, and that the drivers did not slow down or swerve before the collision. The coefficient of kinetic friction is 0.7.

How fast, in ft/s, were the vehicles moving prior to the collision?

(please show work)

Explanation / Answer

For car , velocity after collision = sqrt(2*0.7*9.8*40.34)

                                                    = 23.52 ft/sec

For van , velocity after collision = sqrt(2*0.7*9.8*13.78)

                                                    = 13.75 ft/sec

Also,   3572 * Vcar = 3572 *23.52 *cos37.5 + 4123*13.75*cos66.5

       => Vcar prior to the collision = 25 ft/sec

Also,   4123 * Vvan = 3572 *23.52 *sin37.5 + 4123*13.75*sin66.5

       => Vvan prior to the collision = 25 ft/sec

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