You are driving North through an intersection in a 55 mi/hr speed zone, when the

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 46.2 m with locked wheels at an angle of 67.2° to the East of North. The mass of your car is 1516.0 kg while the Cadillac has a mass 2089.0 kg. The coefficent of sliding friction is 0.60. 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.

Use conservation of momentum.

Compute your speed immediately prior to the collision as evidence for or against the speeding ticket

Explanation / Answer

Given that

The mass of your car is (ma) = 1516.0 kg while the Cadillac has a mass (mb) =2089.0 kg.

The coefficent of sliding friction is(mu)= 0.60

As the two cars are sticked together it is an inelastic collision

From the conservation of momentum

Vb police car is =Sqrt(mudg)sinthea*(ma+mb)/mb =Sqrt(0.60*46.2*9.81)*sin(67.2)(1516+2089)/2089 = 16.490*0.921*1.7257=26.209m/s

Va of your car =Sqrt(mudg)costheta*(ma+mb)/ma =16.490*cos67.2*2.377 =16.490*0.3875*2.2377 =14.299m/s

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