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Neglecting extraneous factors like wind resistance, and given that the human body is only about 25% efficient, how much power p must an 80.0kg runner produce in order to run at a constant speed of 3.55 m/s up a 7.00° incline?

Answer :

Final answer:

To calculate the power that an 80.0 kg runner must produce to run at a constant speed of 3.55 m/s up a 7.00° incline, we can use the formula for power: P = Fv. First, we need to find the force the runner needs to exert to overcome the gravitational force and move up the incline. The gravitational force can be found using the equation: F = mg sin(θ), where m is the mass of the runner, g is the acceleration due to gravity (approximately 9.8 m/s^2), and θ is the angle of the incline. Then, we can calculate the power by multiplying the force by the velocity of the runner: P = Fv.

Explanation:

To calculate the power that an 80.0 kg runner must produce to run at a constant speed of 3.55 m/s up a 7.00° incline, we can use the formula for power: P = Fv. First, we need to find the force the runner needs to exert to overcome the gravitational force and move up the incline. The gravitational force can be found using the equation: F = mg sin(θ), where m is the mass of the runner, g is the acceleration due to gravity (approximately 9.8 m/s^2), and θ is the angle of the incline. Then, we can calculate the power by multiplying the force by the velocity of the runner: P = Fv.



Let's start by calculating the gravitational force:



F = (80.0 kg)(9.8 m/s^2) sin(7.00°)



Next, we can calculate the power:



P = (F)(3.55 m/s)



Using these equations, we can find the power required for the runner to run at a constant speed of 3.55 m/s up a 7.00° incline.

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