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.
The formula to calculate the kinetic energy of any moving body is -
K.E. = [tex]\frac{1}{2} mv^{2}[/tex]
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. = [tex]\frac{1}{2} mv^{2}[/tex]
We know that -
v = [tex]\frac{distance}{time} = \frac{x}{t}[/tex]
Substituting the value of velocity in equation of kinetic energy -
K.E = [tex]\frac{1}{2} m(\frac{x}{t}) ^{2}[/tex]
We can see that the kinetic energy of the athlete is -
K.E. [tex]\alpha\; (\frac{x}{t})^{2}[/tex]
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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