Question

You are driving North through an intersection in a 55 mi/hr speed zone, when the local Chief of Police, who is driving his new Cadillac and approaching the intersection from the West, hits you broadside. The two cars stick together and skid a distance 38.9 m with locked wheels at an angle of 66.9° to the East of North. The mass of your car is 1425.0 kg while the Cadillac has a mass 2088.0 kg. The coefficent of sliding friction is 0.70. The Chief of Police is angry that you have damaged his new Cadillac and gives you a ticket for speeding. The local judge is going to believe his Chief of Police rather than some out-of-town student. You realize that the knowledge you learned in your physics course is your only hope for acquittal. Compute the speed of the Chief of Police immediately prior to the collision. Compute your speed immediately prior to the collision as evidence for or against the speeding ticket.

Answer 1

Total friction force = u (m1 + m2) * g = 0.7 (1425 + 2088) * 9.8 = 24099.18 N

work done by this force = 24099.18 *38.9 = 937458.102 J

this is equal to kinetic energy

1/2mv² =  937458.102

v = 23.102 m/s

Momentum in direction (north) = 3513 * 23.102 * cos 66.9 = 31841.03 Kg m/s

In east, momentum = 74650.25 Kg m/s

Therefore,

Chief of Police's velocity prior to the collision = 74650.25 / 2088 = 35.75 m/s

your speed prior to collision = 31841.03 / 1425 = 22.344 m/s

as speed limit was 55 mi/h or 24.6 m/s, it is clear that it was Chief of Police's fault