Answer: the man consumed 0.539598 Kilo-calories of food
Step-by-step explanation:
Given the data in the question;
first we calculate the work required to raise the given weight at the given height;
ΔW = mgh = w'h = (0.87) × h
= ( 0.87 × 163) × (31/12)ft { 1 foot = 12 inch}
= 366.34 lb-ft
Now since 22% of all the potential energy stored in food is available for useful work;
ΔW = 0.22 × ΔPE
ΔPE = ΔW/0.22
we substitute
ΔPE = 366.34 / 0.22
= 1665.18 lb-ft
Now given that; 1 ft-lb = 0.000324048 Kilocalories
= 1665.18 × 0.000324048
= 0.539598 Kilo-calories
Therefore the man consumed 0.539598 Kilo-calories of food