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 35.6m with locked wheels at an angle of 65.7deg to the East of North. The mass of your car is 1508.0 kg while the Cadillac has a mass 2029.0 kg. The coefficent of sliding friction is 0.80. 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.
it says to use the xonservation of momentum to calculate it

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

Explanation / Answer

Given data:

speed of the car=55mi/hr

mass of the car =1508Kg

mass of the Cadillac =2029Kg

angle=65.7 deg to the east of north

coefficient of slding friction=0.80

frictional force=(coefficient of friction)N

ma=(coefficient of friction)mg

a=0.80*9.8=7.84m/s2

from v2=u2+2as

v2=0+2*7.84*35.6=558.2

v=23.6m/s

final momentum towards east direction is

MVsin(65.7)

(1508+2029)(23.6)(sin(65.7)=76045.5

initial momentum towards east direction is

2029u

equating both momentums

2029u=76045.5

u=76045.5/2029

u=37.47m/s

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