In our analysis of energy costs in transportation, we focussed on the "trip force" associated with stopping and starting, rolling resistance, and air drag and other aerodynamic (or hydrodynamic) effects. However, there is also an energy cost associated with hill-climbing. Suppose that when you drive down a hill, braking causes you to lose a fraction f of the kinetic energy gained by going downhill. Under what circumstances does that energy cost exceed the ordinary flat-road trip cost? That, is what condition can you place on vehicle speed, hill size, stopping distance, and other parameters such that when this condition is satisfied, the "hill force" exceeds the "trip force"? Be sure to identify which parameters are relevant to this question and to construct a quantitative condition.