Fair ticket? You are driving your car uphill along a straight road when suddenly

Question

Fair ticket? You are driving your car uphill along a straight road when suddenly, another car runs a red light and enters the intersection in front of you. You apply your brakes hard and skid in a straight line to a stop, leaving skid marks 100 feet long (your car's antilock braking system didn't work). A police officer observing the incident gives a ticket to the other car for running a red light, but also gives you a ticket for exceeding the speed limit of 30 mph. When you get home, you wonder if the ticket you got was fair. You find in your physics book that the coefficient of static friction between car tires and the road is about 0.8 and the coefficient of kinetic friction is 0.6. You estimate that the hill on which you were driving made an angle of about 10 degree with the horizontal. Your car's owner's manual says that your car weighs 2050 lbs. Was the ticket you got fair?

Explanation / Answer

angle of inclination, theta=10 degrees

coefficient of static friction, us=0.8

coefficient of kinetic friction, uk=0.6

length of the skid mark is l=100ft

weight of the car, w=2050 lbs

speed limit v=30 mph

use,

by using conservation of enegry,

1/2*m*vo^2=m*g*l*sin(theta)+uk*m*g*l*cos(theta)

1/2*vo^2=g*l*sin(theta)+uk*g*l*cos(theta)

1/2*vo^2=32.2*100*sin(10)+0.6*32.2*100*cos(10)

=====>

initial speed of the car is, vo=70.17 ft/sec

or

vo=47.84 mph

hence, vo>v ,answer is no

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