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20 March, 04:13

A world class runner can run long distances at a pace of 15 km/hour. That runner expends 800 kilocalories of energy per hour. a) Find the power (in Watts [W]) the runner is exerting while running. b) Find the total energy (in Joules [J]) exerted by the runner in a 15 km run. c) How many Milky Way (Original Single 52.2g) chocolate bars does the runner need to buy to supply the amount of energy to complete a half-marathon (13.1 miles) ? (Cite your source for the number of calories in a Milky Way bar)

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  1. 20 March, 07:15
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    Answer: a) 1.05kW b) 3.78MJ c) 5.3 bars

    Explanation:

    A)

    Conversions give 900 kcal as 900000 x 4.2 J/cal {4.2 J/cal is the standard factor}

    = 3780kJ

    And 1 hour = 3600s

    Therefore, Power in watts = 3780/3600 = 1.05kW = 1050W

    B)

    At 15km/hour a 15km run takes 1 hour.

    1 hour is 3600s and the runner burns 1050 joule per second.

    Energy used in 1 hour = 3600 x 1050 J/s

    = 3780000 J or 3.78MJ

    C)

    1 mile = 1.61km so 13.1 mile is 13.1 x 1.61 = 21.1km

    15km needs 3.78 MJ of energy therefore 21.1km needs 3.78 x 21.1/15 = 5.32MJ = 5320 kJ

    Finally,

    1 Milky Way = 240000 calories = 4.2 x 240000 J = 1008000J or 1008kJ

    This means that the runner needs 5320/1008 = 5.3 bars
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