I took a physics exam and this question was on the exam. I would like help in re

Question

I took a physics exam and this question was on the exam. I would like help in revisiting the question. The question presented here is an abbreviated form of the question with the key parts:

                         An individual is descending a hill with an 8% grade in a 15,000 kg. truck at 30 m/s..

a.what is the incline

b. When the driver hits the brake he realizes they are broken, there is a emergency truck ramp 1000 m down the incline. At what speed was he going prior to hitting the incline.

c. If the emergency ramp he hits is 15 degrees and the requirement for the ramps is that they have to be twice as long as the average stopping speed, what is the length of the ramp

Explanation / Answer

a)

8 % = 0.08

Incline = atan (0.08) = 4.57 degrees

b)

v^2 = u^2 + 2as where a = g*sin theta = 9.81*sin4.57 = 0.7823 m/s^2

v^2 = 30^2 + 2*0.7823*1000

v = 49.64 m/s

c)

v^2 = u^2 - 2as where a = g*sin theta = 9.81*sin15 = 2.539 m/s^2

0 = 49.64^2 - 2*2.539*s

s = 485.25 m

Actual length = 2*485.25 = 970.5 m

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