You are going 60 mph down a stretch of highway with a 15% downhill grade (meanin

Question

You are going 60 mph down a stretch of highway with a 15% downhill grade (meaning that the rise/run of the incline is 0.15). You see a deer in the road 90 m in front of you and slam on your anti-lock brakes so you maintain maximum braking. The coefficient of static friction between your tires and the wet road is 0.600. Answer the following, sketching the situation along with a free body diagram to support your solution.

a) What is the car's acceleration while braking?

b) At what distance do you come to a complete stop? (Did you hit the deer?)

Explanation / Answer

a) Here ,

for the angle of incline is theta

tan(theta) = 0.15

theta = 8.53 degree

for the acceleration down the hill

a = g * (sin(theta) - u * cos(theta))

a = 9.8 * (sin(8.53 degree) - 0.60 *cos(8.53 degree) )

a = -4.36 m/s^2

the acceleration while braking is -4.36 m/s^2

b) let the distance to stop is d

initial speed ,u = 60 mph = 26.8 m/s

Using third equation of motion

0^2 - 26.8^2 = -2 * 4.36 * d

solving for d

d = 82.5 m

the stopping distance is 82.5 m

No , you didn't hit the deer

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