Question

While driving in the mountains, you notice that when the freeway goes steeply downhill, there are emergency exits every few miles. These emergency exits are straight dirt ramps which leave the freeway and are sloped uphill. They are designed to stop trucks and cars that lose their breaks on the downhill stretches of the freeway even if the road is covered in ice. You are curious, so you stop at the next emergency road. You estimate that the road rises at an angle of 10° from the horizontal and is about 100 yards (300 ft) long. What is the maximum speed of a truck that you are sure will be stopped by this road, even if the frictional force of the road surface is negligible?

Answer 1

Solution:

Gven,

100 yard = 91.44 m
h = 91.44*sin10^o = 15.88 m (height of the ramp)
A vehicle entering the ramp can safely stop if his kinetic energy is less than the increment of potential energy relevant to the h step.
Let v be the limit speed:
(1/2)mv2 = mgh

v = (2gh) = (2*9.81*15.88) = 17.6 m/s

v =17.6 m/s = 17.6*3.6/1.61 = 39.35 miles/h.

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