# Fundamentals of Transportation/Grade/Homework

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## Homework[edit]

1. Determine the maximum grade an empty tractor-trailer with a mass of 10000 kg can climb at a sustained speed of 75 km/h.

The frontal area (A) of the truck is 10 m^{2}, the drag coefficient = 1.00 and the available power is 280 kW, ρ=1.2 kg*m^{-3}, g = 9.81 m*sec^{-2}

2. What is the maximum grade a bicycle can climb at a sustained speed of 12 km/h assuming the following:

- Rho = density of air (1.20 kg*m
^{-3}) - g = 9.81 m*sec
^{-2} - Mass (with bicyclist) = 100 kg
- Nominal Power = 1 kW
- Frontal Area (A) = 1 m
^{2} - Drag Coefficient = 0.5
- Available power = 100 percent of nominal power

- Fr = 0.020 W

3. Bicyclists get tired. Assume the bicyclist slowly loses power (and thus velocity) going up the hill of the grade you just determined in question 2 above. If available power drops continuously from 100% to 0% over the course of the hour, to the nearest kilometer, how far does the bicyclist travel? (Use appropriate approximations.)