The formula used to calculate power is:
Power = Work / Time
Where Work is defined as Force multiplied by Distance, hence:
Power = Force * Distance / Time
This can also be expressed as:
Power = Force * Velocity<span>
Converting the velocity from km/h to m/s:</span>
Velocity = (5 km / h) (1000 m / km) (1 h / 3600 s)<span>
Velocity = 1.39 m/s
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The calculated force corresponds to the vertical component of the hiker's weight:
Force = Wy * g = W * sin θ * g
To find the angle θ, we utilize the slope, which is defined as:
slope = tan θ = ratio of vertical to horizontal distance
tan θ = 0.09
θ = 5.14˚
Thus, we have Force = 68 kg * sin(5.14˚) * 9.8 m/s²<span>
Force = 666.4 * sin(5.14) = 59.73 N
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<span>Now, let's compute the power:
<span>Power = 59.73 N * 1.39 m/s = 82.96 W
Given the hiker's efficiency is at 25%, we can find the metabolic power:
<span>
Metabolic Power = 82.96 W / 0.25 = 331.83 watts </span></span></span>
