While driving in the mountains, you notice that when the freeway goes steeply do

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 about d=100 m long that leave the freeway and are sloped uphill. They are designed to stop trucks and cars that lose their brakes on the downhill stretches of the freeway. You decide to figure out at what angle from the horizontal an emergency exit ramp should rise in order to stop a M=50 metric ton truck going with v=32 m/s , even if the road is covered with ice.

Explanation / Answer

Length of the ramp = 100 m
Mass of the truck = 50*1000 Kg
Initial Velocity, v = 32 m/s

Initial K.E = Final K.E
1/2*Mv^2 = M*g*h
1/2*32^2 = 9.8*h
h = 52.25 m

sin() = 52.25/100
= 31.5o
Angle from the horizontal, = 31.5o

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