A driver in a red Ferrari makes a 911 call to report that he\'s lost his brakes
ID: 1324277 • Letter: A
Question
A driver in a red Ferrari makes a 911 call to report that he's lost his brakes and his car is out of control. A patrol car picks up the call and races to get ahead of the Ferrari. Once he's ahead, he slows up and matches his speed to the Ferrari. As the Ferrari touches bumpers with him, the policeman brakes as hard as he can. Unfortunately, by this time, they are traveling at 60 mph down a 15 degree grade. The Ferrari's curb weight is 1,940 lb and the police cruiser's curb weight is 3,900 lb. The police cruiser normally brake from 60 mph in 250 ft on level ground under maximum braking. How long does it take the policeman to bring the two cars to rest? How far will they be traveled during this time?Explanation / Answer
We first note tha braking force of the police car.
Note that
v^2 = vo^2 + 2ad
which implies that
a = [v^2 - vo^2]/[2d]
where
v = final velocity = 0 m/s
vo = 60 mph = 26.81666667 m/s
d = 250 ft = 76.2 m
Thus,
a = 4.718724482 m/s^2 , police car alone.
Thus, the braking force = ma,
Fbrake = 8346.043302 N
Now, the total mass of the system is
M = total mass = 1940 + 3900 lb = 2648.526077 kg
Now, the summation of forces is
Fx = Mgsin15 - Fbrake = Ma
Thus,
a = gsin15 - Fbrake/M
Therefore,
a = -0.614776351 m/s^2
Thus, as t = (v - vo)/a, vo = 26.817 m/s,
t = 43.6 s [ANSWER, PART A]
Thus, if they are at 60 mph = 26.817 m/s initially, d = vo^2/2a:
d = 585 m [ANSWER, PART B]
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