That in a moment. But first, I heard on a sports radio show that for the upcoming Super Bowl game the Patriots are favored by 3 points. They also said that the over/under for total points that both teams would score was 57 (as I recall. It was a few days ago.) That is, you can bet that both teams combined will score more than 57 points or you can bet they'll score less. Of course I thought, "Hey, nice system of equations problem."
If x is the points scored by the Atlanta Falcons and y is the number of points scored by the New England Patriots, then we have:
y = x+3 and x+y = 57
That leads to x+(x+3) = 57
So, 2x+3 = 57
So, x = 27 and y = 30
Thus the odds makers are figuring: New England 30, Atlanta 27.
Now, back to: Is it possible to throw a ball 100 yards?
You can look back on the last post to fill in what you might have missed, but currently we are at this formula.
d = (v2/g)ᆞ(sin(2θ))
The distance we are hoping to cover is 100 yards, which is 300 feet. The optimal throwing angle is 45 degrees. The acceleration due to gravity is 32. So,
300 = (v2/32)ᆞ(sin(2(45)))
Solving this gives us v = 97.98 feet per second which is 66.8 miles per hour.
I thought this should be possible. Ater all, there are people that throw a baseball over 100 mph. Surely someone could throw at 66.8 mph. Yes, footballs are heavier and probably have more air resistance, but still...
Turns out that 60 mph is about the best anyone is going to be able to do. You can check it out here
http://ftw.usatoday.com/2014/03/how-fast-football-throw-nfl-combine-logan-thomas. They've tested it out and no one has done better than that in the times they've been keeping track. Maybe someday someone will come a long that throws a football a lot faster than anyone else. But until then the longest passes will be well under 100 yards.
