Question

While running, a person dissipates about 0.60 j of mechanical energy per step per kilogram of body mass. if a 51-kg person develops a power of 67 w during a race, how fast is the person running? (assume a running step is 1.5 m long.)?

Answer 1

Answer:

The speed of the person is 3.27 m/s.

Explanation:

Given that,

Mass of runner = 51 kg

Power = 67 W

Energy = 0.60 J

1 step = 1.5 m

We need to calculate the dissipates energy for 51 kg runner

$\Delta E_{step}= 0.60\times51$

$\Delta E_{step}=30.6\ J$  

We need to calculate the total energy

Using formula of total energy

$\Delta E_{total}=\Delta E_{step}\times S$

The power is,

$P_{avg}=\dfrac{\Delta E_{total}}{\Delta t}$

Put the value of $\Delta E_{total}$

$P_{avg}=\dfrac{\Delta E_{step}\times S}{\Delta t}$

Multiply each side by$\dfrac{1}{E_{step}}$

$\dfrac{P_{avg}}{E_{step}}=\dfrac{S}{\Delta t}$

Put the value into the formula

$\dfrac{S}{\Delta t}=\dfrac{67}{30.6}$

$\dfrac{S}{\Delta t}=2.18$

$S=2.18\Delta t$

We need to calculate the speed of the person

Using formula of speed

$v =\dfrac{d}{t}$

Here, $d = S\times1.5$

$v=\dfrac{S\times1.5}{\Delta t}$

Where, d = distance

t = time

Put the value into the formula

$v=\dfrac{2.18\times\Delta t\times1.5}{\Delta t}$

$v= 2.18\times1.5$

$v=3.27\ m/s$

Hence, The speed of the person is 3.27 m/s.

Answer 2

Given: 0.6J/1.5m/kg
For the particular person, since he is 51kg, every step he ran would yield 30.6J
67 W = 67J/S
Time= 30.6J / 67J/s = 0.4567164179s
Speed = 1.5m / 0.4567164179s
= 3.28m/s