Final answer:
The largest constant speed a 2000 kg Mercedes can sustain going up a 30-degree incline with 100 kW power output is found by calculating the gravitational force component down the slope and equating it to the engine's power output to determine speed.
Step-by-step explanation:
You are looking to find the largest constant speed a 2000 kg Mercedes can sustain going up Pike’s Peak, with an engine delivering energy at a rate of 100 kW, on a road at a 30-degree incline neglecting air resistance. To find this, we need to calculate the force of gravity acting down the slope and equate the power used to overcome this force to the power supplied by the engine at the constant speed.
The force of gravity down the slope (gravitational force component) is given by Fg = m * g * sin(θ), where m is the mass of the car, g is acceleration due to gravity, and θ is the angle of the incline. The power (power output) required to move the car at constant speed is given by P = Fg * v, where P is the power and v is the speed of the car.
Therefore, by rearranging the formula to solve for v, v = P / Fg, and substituting the values given, we can calculate the maximum constant speed the car can sustain on the incline.