If a 30001b car is traveling up a hill and experiences 2001b

If a 30001b car is traveling up a hill and experiences 2001bs of grade resistance, what is the grade of the hill? If the same car travels down another hill and experiences -4001bs of grade resistance, what is the grade of that hill?

Solution

The grade resistance F of a car traveling up or down a hill is modeled by the equation F = W sin , where W is the weight of the car and is the angle of the hill\'s grade ( > 0 for uphill travel, < 0 for downhill travel)

Uphill . So, F = Wsin(theta)

200 = 3000sin(theta)

sin(theta) = 2/30 = 0.067

Grade of hill = sin^-1(0.067) = 3.82 deg

Down hill:

-F = Wsin(theta)

-400 = 3000sin(theta)

sin(theta) = -0.133

Grade of hill : theta = -7.67