5. You are driving North through an intersection in a 55 speed zone, when the lo

Question

5. You are driving North through an intersection in a 55 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 48.4 with locked wheels at an angle of 65.1° to the East of North. The mass of your car is 1450.0 while the Cadillac has a mass 2028.0 . 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

here,

skidding distance = 48.4 m
ma = 1450 kg
mc = 2028 kg
us = 0.60

as
Fn = (ma + mc)*g
Fn = (1450+2028)*9.8
Fn = 34084.4 N

Frictional Force = uN
Ff = 0.6 *34084.4
Ff = 20450.64 N

Work done by Frictional force = Kinetic energy of system
ff.D = 0.5 * (ma + mc) * v^2
20450.64 * 48.4 = 0.5 * (1450+2028) * v^2

v = sqrt( (20450.64 * 48.4)/(0.5 * (1450+2028)) )
v = 23.857 m/s

North momentum :
Pn = (ma + mc)*v *Cos65.1
Pn = (1450+2028)*23.857 * 0.421
Pn = 34932.325 kg.m/s

East momentum :
Pe = (ma + mc)*v *Sin65.1
Pe = (1450+2028)*23.857*0.909
Pe = 75423.953 kg.m/s

PreCollision North Velocity :
Va = Pn/ma
Va = 34932.325 / 1450
Va = 24.091 m/s
Va = 53.89 mph

PreCollision East Velocity :
Vc = Pn/ma
Vc = 75423.953 / 2028
Vc = 37.191 m/s
Vc = 83.194 mph

as you can Speed of cadillac is over the limit of 55 mph

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