A 64 kg hiker climbs to the top of a 3700 m-high mountain. The climb is made in 5.5 h starting at an elevation of 2900 m. Calculate the average power output in watts. Calculate the average power output in horsepower & Calculate assuming the body is 14% efficient, what rate of energy input was required. Answers should be in two significant figures. Please HELP!!!!
Divide the hiker's gain in gravitatIonal potential anergy (M g H) by the elapsed time in seconds (19800).
For the scond part, divide the first answer by 0.14.
To calculate the average power output of the hiker, we can use the formula:
Power = Work / Time
First, let's calculate the work done by the hiker. Work is given by the equation:
Work = Force x Distance
The force exerted by the hiker can be calculated using the equation:
Force = Mass x Gravitational acceleration
Where the mass of the hiker is 64 kg and the gravitational acceleration is approximately 9.8 m/s².
Hence, the force exerted by the hiker is:
Force = 64 kg x 9.8 m/s² = 627.2 N
Now, let's calculate the distance the hiker has climbed. The change in elevation is given by the equation:
ΔElevation = Final Elevation - Initial Elevation
ΔElevation = 3700 m - 2900 m = 800 m
To convert this to distance, we can use the equation:
Distance = ΔElevation + Total Horizontal Distance
It is not mentioned if there is any horizontal distance covered during the climb, so for simplicity, we'll assume it to be zero. Therefore,
Distance = 800 m
Now we can calculate the work done by the hiker:
Work = Force x Distance = 627.2 N x 800 m = 501,760 J
Next, we can calculate the average power output by dividing the work by the time taken:
Time = 5.5 h = 5.5 x 3600 s ≈ 19,800 s
Power = Work / Time = 501,760 J / 19,800 s ≈ 25.34 W
Therefore, the average power output of the hiker is approximately 25.34 watts.
To calculate the average power output in horsepower, we can use the conversion factor:
1 horsepower (hp) = 745.7 watts
Hence,
Power (in horsepower) = Power (in watts) / 745.7 ≈ 0.034 hp
Therefore, the average power output of the hiker is approximately 0.034 horsepower.
Lastly, assuming the body is 14% efficient, we can calculate the rate of energy input required. Efficiency is given by the equation:
Efficiency = (Output power / Input power) x 100
Rearranging the equation, we can solve for input power:
Input power = Output power / (Efficiency / 100)
Input power = 25.34 W / (14 / 100) ≈ 181 W
Therefore, assuming a 14% efficiency, the rate of energy input required is approximately 181 watts.