Question

While running, a person dissipates about 0.60 J of mechanical energy per step per kilogram of body mass. If a 61 kg person develops a power of 65 W during a race, how fast is the person running? Assume that a running step is 1.5 m long.

Answer 1

2.66m/s

Step-by-step explanation:

information we have

power: 65W

work per step per kilogram: 0.60J

mass: 61kg

length of a running step: 1.5m

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the formula for power is:

`P=(W)/(t)`

where W is the work and t is time.

time is also defined as:
`t=(distance)/(velocity)=(d)/(v)`

so substituting this into the formula for power we get:

`P=(W*v)/(d)`

where v is the velocity we are looking for, d is the distance per step:
`d=1.5m`, W is the work per step and P is power
`P=65W`.

we know that the work per step per kilogram is:

0.60J

so to find the work per step of his whole body we need to multiply the 0.60J by the 61 kilograms of his mas:

`W=0.60J*61kg\\W=36.6J`this is the work per step of the person.

So now we can calculate the velocity using the formula for power

`P=(W*v)/(d)`

clearing for v:

`v=(P*d)/(W)\\`

and substituting known values:

`v=((65W)(1.5m))/(36.6J)= 2.66m/s`