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A lot of people are speculating about Aaron Rodgers' game winning pass last night, so I watched the highlight reel and did some math. There are a few things I ignored, namely height from which the ball was thrown and caught, and aerodynamics. Since the units can get pretty weird, I used Wolfram Alpha to try to avoid mistakes.
Distance: Aaron releases the ball at about the GB 36, and Richard makes the catch about 3 yds deep into the end zone. That's a 67yd flight.
Hang time: This is a little trickier. I used a stop watch while watching the video (I have no way of going frame by frame). I got a total hang time of 4.1 Seconds. Meanwhile, the top punter for hang-time in the 2014 season averaged 4.8 seconds One punter even averaged less than 4 seconds.
Height: Assuming half the flight is ascending (I know it's actually more since Richard caught the ball at the top of a jump), we can find that the apex height is (t/2)2 g, which gives us a height of 67.6 ft above whatever height Aaron released the ball. That's about 7.6 stories!
Throw speed: The horizontal velocity is 67yd/4.1 sec =33.4 mph, but it was at a pretty steep angle, so we need to find the initial vertical velocity as well: v=(t/2)g= 45mph. Putting those together we get the release speed s=sqrt(v_x2 + v_y2) = 56mph.
Angle: You'll notice that the vertical is higher than the horizontal. The actual angle that Aaron launched the ball is tan-1 (v_y/v_x)= 53o above horizontal. This means that Rodgers could theoretically hurl the ball even further down the field (at the cost of some of that sweet, sweet hang-time).
Comparison to baseball: A regulation football weighs 14-15 oz. A regulation baseball weighs 5-5.25oz. Assuming the same kinetic energy e=1/2 mv2 , Rodgers' pass was the equivalent of a 91-97(!)mph pitch, depending on the weights of the respective balls, all while maintaining a tight spiral.
The fan angle from sideline seats was also ridiculous.