To measure the force of friction on a moving car, engineers turn off the engine and allow the car to coast down hills of known steepness. The engineers collect the following data: 

1. On a 2.87° hill, the car can coast at a steady 20 m/s. 

2. On a 5.74° hill, the steady coasting speed is 30 m/s. 

The total mass of the car is 1000 kg. 

(a) What is the force of friction at 20 m/s (F₂₀) and at 30 m/s (F₃₀)? 

(b) How much useful power must the engine deliver to drive the car on a level road at steady speeds of 20 m/s (P₂₀) and 30 m/s (P₃₀)? 

(c) At full throttle, the engine delivers 40 kW. What is the angle of the steepest incline up which the car can maintain a steady 20 m/s?

(d) Assume that the engine delivers the same total useful work from each liter of gas, no matter what speed. At 20 m/s on a level road, the car goes 12.7 km/L. How many kilometers per liter does it get if it goes 30 m/s instead?