The Kinetic energy of the athlete will be 50 times of the mass of the athlete.
We have a athlete who completed a 100m race in 10 seconds.
We to estimate the average kinetic energy of the athlete.
What is the formula to calculate the Kinetic energy of any moving body?
The formula to calculate the kinetic energy of any moving body is -
K.E. = \(\frac{1}{2} mv^{2}\)
According to question -
Distance covered by athlete = 100 meters
Time taken by the athlete = 10 seconds
Let's assume the mass of the athlete = M Kg
Consider the formula for the Kinetic energy of the body -
K.E. = \(\frac{1}{2} mv^{2}\)
We know that -
v = \(\frac{distance}{time} = \frac{x}{t}\)
Substituting the value of velocity in equation of kinetic energy -
K.E = \(\frac{1}{2} m(\frac{x}{t}) ^{2}\)
We can see that the kinetic energy of the athlete is -
K.E. \(\alpha\; (\frac{x}{t})^{2}\)
Greater the square of the ratio of x and t, greater will be the kinetic energy.
K.E. = 0.5 x M x 10 x 10
K.E. = 50M
Hence, the Kinetic energy of the athlete will be 50 times of the mass of the athlete.
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