Alexander, who weighs 150 lb, decides to climb Mt. Krumpett, which is 5710 m hig

Question

Alexander, who weighs 150 lb, decides to climb Mt. Krumpett, which is 5710 m 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? Enter the exact answer to two significant figures.

Explanation / Answer

mass = 150 lb = 68 kg

potential energy = m g h

                          = 68 x 9.81 x 5710 x 10^-3

                          = 3811.2 kJ

total energy needed = 7622.4 kJ

Energy from fat = 10 x 38 = 376.56 kJ

energy from protein = 40 x 17 = 668.8 kJ

energy from carbohydrates = 50 x 17 = 836.8 kJ

total energy = 376.56 + 668.8 + 836.8

                    = 1882.16 kJ

number of bars needed = 3811.2 / 1882.16

                                    = 2.0

number of bars needed = 2.0

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