Final answer:
To calculate the power an 80.0kg runner must produce to run up a 7.00° incline at a constant speed of 3.55 m/s, we use the work done against gravity and consider the body's 25% efficiency. The multiple choice options given are incorrect because power is measured in watts, not meters per second.
Step-by-step explanation:
To determine how much power P an 80.0kg runner must produce to run up a 7.00° incline at a constant speed of 3.55 m/s, we will consider the work done against gravity. The power output calculated is the mechanical power required for the uphill movement, but since the human body is only about 25% efficient, the actual power produced by the body will be four times the mechanical power.
The power P needed to climb the incline can be calculated using the formula:
P = (m × g × h) / t,
where:
m is the mass of the runner (80.0kTo find h, we use the sine of the incline angle θ:
h = v × sin(θ),
where v is the speed (3.55 m/s), and θ is the incline angle (7.00°).
Once we calculate the mechanical power, we take into account the 25% efficiency by dividing the mechanical power by 0.25. Substituting the given values and solving will provide the power output required by the runner. However, none of the multiple choice options (1) 10 m/s, (2) 20 m/s, (3) 30 m/s, (4) 40 m/s are correct since power is not measured in meters per second but in watts (W).