Answer:
[tex]4265.04\ \text{m}[/tex]
[tex]2.38\times 10^{10}\ \text{W}[/tex]
Explanation:
PE = Energy of food = 500 cal = [tex]500\times4184=2.092\times10^6\ \text{J}[/tex]
m = Mass of object = 50 kg
g = Acceleration due to gravity = [tex]9.81\ \text{m/s}^2[/tex]
Potential energy of food is given by
[tex]PE=mgh\\\Rightarrow h=\dfrac{PE}{mg}\\\Rightarrow h=\dfrac{2.092\times 10^6}{50\times 9.81}\\\Rightarrow h=4265.04\ \text{m}[/tex]
Nancy could raise the weight to a maximum height of [tex]4265.04\ \text{m}[/tex].
Mass of [tex]H_2[/tex] used per year = [tex]25\times 10^{9}\ \text{kg/year}[/tex]
Energy of [tex]H_2[/tex] = [tex]\dfrac{30\times10^9}{1000}=30\times 10^6\ \text{J/kg}[/tex]
Power
[tex]P=25\times 10^{9}\ \text{kg/year}\times 30\times 10^6\ \text{J/kg}\\\Rightarrow P=7.5\times 10^{17}\ \text{J/year}\\\Rightarrow P=\dfrac{7.5\times 10^{17}}{365.25\times 24\times 60\times 60}\\\Rightarrow P=2.38\times 10^{10}\ \text{W}[/tex]
The power requirement is [tex]2.38\times 10^{10}\ \text{W}[/tex].
