Question

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. (3 points) b) Find the total energy (in Joules [J]) exerted by the runner in a 15 km run. (3 points) Answer:

Answer 1

Answer:

(a) 933.33W

(b) 3.36 x 10⁶J

Explanation:

(a) Power is the time rate of change of energy.

In the question, the runner expends 800 kilocalories (kcal) of energy in one hour (h).

That means that power expended is 800 kcal / h.

To get the power in Watts, we convert 800 kcal/h to Joules per second (J/s) as follows;

(i) First convert kcal to Joules (J)

1 cal = 4.2 J

1 kcal = 1 x 1000 cal = 1 x 1000 cal x 4.2 J / 1 cal = 4200 J

(ii) Then convert 1 hour to second (s)

1 h = 3600s

(iii) Now convert 800 kcal/h to J/s

800 kcal / h = $\frac{800 * 1 k cal}{1 h}$ = $\frac{800 * 4200J}{3600s}$ = 933.33J/s = 933.33W

Therefore, the power expended in J/s (or in Watts) is 933.33

(b) According to the question, the runner can run 15km in 1 hour and will expend a power of 933.33W. To calculate the energy expended at this time, we use the formula;

E = P x t             -------------------(ii)

Where;

E = Energy

P = Power = 933.33W

t = time taken = 1 hour = 36000s

Substitute these values into equation (ii) as follows;

E = 933.33 x 3600

E = 3359988 J

E = 3.36 x 10⁶ J

Therefore, the total energy is 3.36 x 10⁶J