A world class runner can run long distances at a pace of 15 km/hour. That runner expends 800 kilocalories of energy per hour. 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)?

a) Power is the rate of use of energy per unit time. This is given in the question as 800 kilocalories per hour. Part a) requires the power in Watts (W) which is equivalent to Joules per second. Thus, kilocalories per hour need to be converted to Joules per second:

[tex]1kcal = 4184J[/tex]

[tex]1hour = 3600s[/tex]

[tex]power=\frac{energy}{time}[/tex]

[tex]power=\frac{800kcal*\frac{4184J}{kcal}}{1hour*\frac{3600s}{hour}}[/tex]

[tex]power=\frac{3347200}{3600}[/tex]

[tex]power=929.78J/s=929.78W[/tex]

b) Total time required for a 15km run can be calculated by the speed of the runner (15km/h):

[tex]time=\frac{distance}{speed}[/tex]

[tex]time=\frac{15km}{15km/h}[/tex]

[tex]time=1hour=3600s[/tex]

The energy exerted over this time can be found by:

[tex]energy=power*time[/tex]

[tex]energy=929.78J/s*3600s[/tex]

[tex]energy=3,347,200J[/tex]

c) Total time required for a 13.1mile run can be calculated by the speed of the runner (15km/h):

[tex]1mile=1.6km[/tex]

[tex]time=\frac{distance}{speed}[/tex]

[tex]time=\frac{13.1mile*\frac{1.6km}{mile}}{15km/h}[/tex]

[tex]time=\frac{20.96}{15}[/tex]

[tex]time=1.40h=5030.4s[/tex]

The energy exerted over this time can be found by:

[tex]energy=power*time[/tex]

[tex]energy=929.78J/s*5030.4s[/tex]

[tex]energy=4,677,165J[/tex]

Assuming one Milky Way (Original Single 52.2g) has 240 kilocalories

[tex]number=\frac{energy}{energy_{milkyway}}[/tex]

[tex]number=\frac{4677165}{240kcal*\frac{4184J}{kcal}}[/tex]

[tex]number=\frac{4677165}{1004160}[/tex]

[tex]number=4.65[/tex]

5 milkyway bars are needed