Alexander, who weighs 198lb , decides to climb Mt. Krumpett, which is 5850m high

Question

Alexander, who weighs 198lb , decides to climb Mt. Krumpett, which is 5850m high. For his food supply, he decides to take nutrition bars. The label on the bars states that each 100-g bar contains 10 g of fat, 40 g of protein, and 50 g of carbohydrates.

One gram of fat contains 9 Calories, whereas each gram of protein and carbohydrates contains 4 Calories.

Alexander wants to know exactly how many bars to pack in his backpack for the journey. To provide a margin of safety, he assumes that he will need as much energy for the return trip as for the uphill climb. How many bars should Alexander pack?

Explanation / Answer

198 lbs = 89.813 kg

Heigth = 5850 m

Potential Energy = mgh = 89.813 * 9.8 * 5850 = 5148979.2 J

Energy required = 2 * 5148979.2 = 10297958.4 (going up and coming back is same)

Energy in 1 bar

= 10 * 9 + (40 + 50)*4 = 90 + 360 = 450 Cal

= 450 * 4.12 = 1854 J

Number of Bars Required = 10297958.4 / 1854 = 5555 bars

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