Answer:
[tex]1.9\times 10^5\ J[/tex]
[tex]1.8\times 10^{2}\ kcal[/tex]
[tex]1.3\times 10^{2}\ kcal[/tex]
[tex]1.2\times 10^{3}\ W[/tex]
Explanation:
m = Mass of person = 60 kg
g = Acceleration due to gravity = 9.81 m/s²
t = Time taken = 10 min and 49 s
Total height
[tex]h=3.7\times 86\\\Rightarrow h=318.2\ m[/tex]
Potential energy is given by
[tex]U=mgh\\\Rightarrow U=60\times 9.81\times 318.2\\\Rightarrow U=187292.52\ J[/tex]
The gravitational potential energy is [tex]1.9\times 10^5\ J[/tex]
The energy in the climb
[tex]\dfrac{187292.52}{0.25}=749170.08\ J[/tex]
Converting to kcal or Cal
[tex]\dfrac{749170.08}{4184}=179.05594\ kcal[/tex]
The amount of energy used to climb [tex]1.8\times 10^{2}\ kcal[/tex]
Amount gone to heat
[tex]179.05594\times 0.75=134.291955\ kcal[/tex]
The amount burned [tex]1.3\times 10^{2}\ kcal[/tex]
Power is given by
[tex]P=\dfrac{E}{t}\\\Rightarrow P=\dfrac{749170.08}{10\times 60+49}\\\Rightarrow P=1154.34526\ W[/tex]
The power is [tex]1.2\times 10^{3}\ W[/tex]
