Roberto Carlos - Goal!!

Carlos kicked the ball with the outside of his left foot to make it spin anticlockwise as he looked down onto it. Conditions were dry, so the amount of spin he gave the ball was high, perhaps over 10 revolutions per second. Kicking it with the outside of his foot allowed him to hit the ball hard, at probably over 30 ms–1 (70 mph). assume that the ball pushed away all the air at the front half area to the anti-clockwise direction. also assume that the air pushed is a layer of 3cm thickness. the ball will follow a circular orbit.

What is the radius R from the ball path in the air?

Details And Assumptions:

-The air density 1 $kg/m^3$ .

-The ball speed v=29.2 $m/s$ .

-The balls' angular velocity $\omega = 69.11 Rad/s$

-Neglect the pushed away air from the back side of the ball.

-The pushed away air particles are perpendicular to the ball radius.

-Neglect the losses to the liner or angular velocity.

-The ball mass is 420g.

-The ball radius 11cm.

report you answer as ⌊R⌋.