driving North through an intersection in a 55 mph speed zone, Police, who is dri

Question

driving North through an intersection in a 55 mph speed zone, Police, who is driving is new Cadillac and approaching the intersection from the West, hits you broadside. The two cars stick together and skid a distance 46.2 mwith 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.

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

Explanation / Answer

given,

mass of cadillac = 2089 kg

mass of car = 1616 kg

speed zone = 55 mph or 24.5872 m/s

frictional force = k * (m1 + m2) * g

frictional force = 0.6 * (1516 + 2089) * 9.8

frictional force = 21197.4 N

force = ma

21197.4 = (1516 + 2089) * a

a = 5.88 m/s^2

v^2 = u^2 + 2as

0 = u^2 - 2as

0 = u^2 - 2 * 5.88 * 46.2

u = 23.31 m/s

by conservation of momentum

initial horizontal momentum = final horizontal momentum

2089 * v = (1516 + 2089) * 23.31 * sin(67.2)

speed of the Chief of Police immediately prior to the collision v = 37.0831 m/s

initial vertical momentum = final vertical momentum

1516 * v_n = (1516 + 2089) * 23.31 * cos(67.2)

speed immediately prior to the collision v_n = 21.48 m/s which is less than the speed zone limit of 24.5872 m/s

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