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January 31, 2015

January 31, 2015

Posted by **Physics/Math** on Friday, February 23, 2007 at 2:47am.

Integrate the force vs time function during the period of contact. This will tell you the momentum delivered to the ball.

Impulse = Integral of a t- b t^2

from t = 0 to t = 2*10^-3 s,

where

a = 5*10^6 and b = 2.5*10^9

The integral is at^2/2 - bt^3/3.

Evaluate it at the limits of integration and take the difference.

The average force is the impulse divided by the time of contact.

The maximum force occurs when f'(t) is zero, which is when

a = 2 b t

t = a/(2 b) = 1.0*10^-3 s.

The ball's velocity when it leaves the foot = (momentum change)/mass = (impulse)/mass

(since the initial momentum is zero)

Great...I got it. Thanks :)

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