Complete question is: While running, a person dissipates about 0.60 J of mechanical energy per step per kilogram of body mass. If a 60-kg person develops a power of 70 W during a race, how fast is the person running? (Assume a running step is 1.5 m long).
Answer: The person running at a speed of 2.91 m/s.
Explanation:
Given: Mass of runner = 60 kg
Runner dissipates = 0.6 J/kg per step
Average power = 70 W
1 step = 1.50 m
Energy dissipated by the runner is as follows.
[tex]\Delta E_{step} = 0.60 \times 60\\= 36 J[/tex]
Formula used to calculate the value of one step 'S' is as follows.
[tex]\frac{S}{\Delta t} = \frac{P_{avg}}{\Delta E_{step}} = \frac{70}{36}\\= 1.94\\S = 1.94 \Delta t[/tex]
It is known that average velocity is equal to the total distance divided by time interval.
So, total distance for the given situation is as follows.
[tex]d = S \times 1.5[/tex]
Hence, speed of the person is calculated as follows.
[tex]v_{avg} = \frac{d}{\Delta t}\\= \frac{S \times 1.5}{\Delta t}\\= \frac{1.94 \Delta t \times 1.5}{\Delta t}\\= 2.91 m/s[/tex]
Thus, we can conclude that the person running at a speed of 2.91 m/s.
