A physics and philosophy of the mind football question:
I am sure you have heard that the New England Patriots have been found to have deflated the footballs in the game Sunday -by some reports 2 pounds of air pressure – to throw off the Colts and to give the Patriots the edge in winning the game. The ball let’s assume thus weighted 2 pounds instead of 4 pounds. This made it highly problematic for Luck to throw the ball accurately. Apparently or lets assume Brady had been practicing with a ball deflated by 2 pounds for weeks. Here is my question –
Word problem: A receiver for the Colts can run 40 yards in 4 seconds. He runs a pattern that takes him up the field 40 years then he cuts across 20 yards and then up toward the goalpost for 10 yards. Luck takes the ball and drops back 10 yards. So he is throwing the pass around 60 yards, Assuming the receiver runs the pattern in just over 7 seconds then Luck must throw the ball at a velocity and with enough force for it to travel 7 seconds in 60 yards. But the ball weights 2 pounds instead of 4, and the air pressure is lower so assume no wind speed resistance and the pull of gravity at 9.8m1x2 x weight and assume a normal vector on the ball he would normally throw that weighted 4 pounds. What would be the formula to sort out the impact of the 2 pound as opposed to 4 pound ball on how the quarterback would have to throw the ball? How would the drag work? Would Brady be throwing the ball harder or softer knowing he was throwing a 2 pound vs a 4 pound ball?
Additional Points provided by James Dow, Philosopher of the Mind, Hendrix College
James has an interest in sports psychology. He points out that the minds of both quarterbacks would have over the years been conditioned to throw the 4 pound ball. Thus creating a natural ingrained conditioned action in the mind telling the body the amount of shoulder and arm muscle strength, body, foot position etc that each would use in throwing such a pass. The question is could Bradley have unlearned this in two weeks?