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 36.0 m with locked wheels at an angle of 58.3° to the East of North. The mass of your car is 1565.0 kg while the Cadillac has a mass 1924.0 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

Let the initial speed of cop car be u m/s

Finding the final velocity of the system after collision

M=sum of mass of both cars,

s= distance travelled by skidding= 36 m, final velocity of system, U =0

velocity of system just after collision, V=(to be found)

frictional force/M= acceleration,a

a=f/M=*M*g/M= *g=0.6*9.8= 5.88 m/s2 (a is negative here)

V2-U2=2*a*s

V=20.57 m/s

Total momentum in east before collision = 1924*u

given, theta=58.3 degrees, M=1924+1565=3489 kg

V=20.57 m/s

Total momentum in east after collision = M*V* sin(theta)

=3489*20.57*sin(58.3)=61061.63

Equating both the momentums in east directions

61061.63=1924*u

u=31.73 m/s

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