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
[tex]\Delta E_{step}= 0.60\times51[/tex]
[tex]\Delta E_{step}=30.6\ J[/tex]
We need to calculate the total energy
Using formula of total energy
[tex]\Delta E_{total}=\Delta E_{step}\times S[/tex]
The power is,
[tex]P_{avg}=\dfrac{\Delta E_{total}}{\Delta t}[/tex]
Put the value of [tex]\Delta E_{total}[/tex]
[tex]P_{avg}=\dfrac{\Delta E_{step}\times S}{\Delta t}[/tex]
Multiply each side by[tex]\dfrac{1}{E_{step}}[/tex]
[tex]\dfrac{P_{avg}}{E_{step}}=\dfrac{S}{\Delta t}[/tex]
Put the value into the formula
[tex]\dfrac{S}{\Delta t}=\dfrac{67}{30.6}[/tex]
[tex]\dfrac{S}{\Delta t}=2.18[/tex]
[tex]S=2.18\Delta t[/tex]
We need to calculate the speed of the person
Using formula of speed
[tex]v =\dfrac{d}{t}[/tex]
Here, [tex]d = S\times1.5[/tex]
[tex]v=\dfrac{S\times1.5}{\Delta t}[/tex]
Where, d = distance
t = time
Put the value into the formula
[tex]v=\dfrac{2.18\times\Delta t\times1.5}{\Delta t}[/tex]
[tex]v= 2.18\times1.5[/tex]
[tex]v=3.27\ m/s[/tex]
Hence, The speed of the person is 3.27 m/s.
