**P. 4662.** The goal-keeper is just about to kick off the ball. The kick lasts for \(\displaystyle \Delta
t=0.01\) s, during which the goalkeeper exerts an average force of \(\displaystyle F=850\) N on the ball lying on the ground. If there is no air drag, the kicked ball would reach the ground in \(\displaystyle t=3\) s and it would be \(\displaystyle \ell=45\) m further.

\(\displaystyle a)\) What is the greatest height that the ball could reach?

\(\displaystyle b)\) According to the official rules of association football the mass of the ball must be between 410 g and 450 g. Is the match played according to the rules?

(4 points)

**Deadline expired on 10 November 2014.**