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THE FASTEST MAN ON THE EARTH: 

THE FASTEST MAN ON THE EARTH

How Powerful is Usain ?: 

How Powerful is Usain ? ? = You are about to find out !

The Steps: 

The Steps Obtain actual measurements of Usain’s speed Get an empirical formula for speed that fits the measurements Identify the relevant laws of physics Derive the formula for speed from the physical laws Get the value of the power by comparing the empirical formula with derived one Calculate the air resistance

Physical laws of running -1: 

Physical laws of running -1 Newton’s 2 nd law of motion The force exerted by the ground on usain (the reaction of his pushing on the ground, from newton’s third law)

Physical laws of running -II: 

Physical laws of running -II The power equation Apply this formula to Usain : power generates is equal to the force the ground exerts on him times his speed

Basic assumption – Constant power: 

Basic assumption – Constant power = Constant We assume that Usain generates constant power over the entair length of his run. an assmuption on frequently made in the physics of running. Constant power means that as his speed increases, the force he exerts decreases portionally

Deriving the speed formula: 

Deriving the speed formula F = m a V = [2 Z] ½ t ½ FV = maV X = ( 8Z - 9) ] ½ t ½ P = maV V = [ 3 Z] 1/3 t 1/3 V dV/dt = P/m P/m = Z (zip) Solving for t is function of X and substituting it in the formula for V. we get V as a function of X to the one third power. This is the formula that we will compare with the empirical One.

Comparing the formulas: 

Comparing the formulas From the empirical data From the laws of motion V = 4.163 x 1/3 V = [3z] 1/3 x 1/3 4.163 = [3Z] 1/3 Equating the Coefficients of X 10 to the third, we get an equation for z.

Sloving for the Power : 

Sloving for the Power Z = 24.058 P = mZ = 90 * 24.058 P = 2165 W P = 2.9 hp Which ofter dividing by 746 . Is 2.9 horse power

Equivalent HorsePower: 

Equivalent HorsePower =

Calculating the Air Resistance: 

Calculating the Air Resistance