A 64-kg hiker climbs to the top of a 3700 m-high mountain. The climb is made in 5.5 hr starting at an elevation of 2900 m. Calculate the average power output in watts. a. Calculate the average power o

To calculate the average power output, we can use the formula: Power = Work / Time The work done by the hiker is equal to the change in potential energy: Work = mgh where m is the mass of the hiker, g is the acceleration due to gravity (9.81 m/s^2), and h is the change in height (3700 m - 2900 m = 800 m). Work = (64 kg)(9.81 m/s^2)(800 m) = 502,784 J The time taken to climb the mountain is 5.5 hours = 19,800 seconds. Average Power = Work / Time = 502,784 J / 19,800 s = 25.4 W a. To convert watts to horsepower, we can use the conversion factor: 1 hp = 746 W Average Power in horsepower = 25.4 W / 746 W/hp = 0.034 hp b. The rate of energy input required can be calculated using the efficiency of the body. We can assume that 14% of the energy input is converted to useful work, and the rest is dissipated as heat. Useful work = Work done x Efficiency = 502,784 J x 0.14 = 70,392 J The time taken to do the work is 5.5 hours = 19,800 seconds. Rate of energy input = Useful work / Time = 70,392 J / 19,800 s = 3.55 W Again, using the conversion factor: Rate of energy input in horsepower = 3.55 W / 746 W/hp = 0.0048 hp Therefore, the average power output of the hiker is 25.4 watts, or 0.034 horsepower, and the rate of energy input required, assuming 14% efficiency, is 3.55 watts or 0.0048 horsepower.