Aaron Rodgers is good, but how good is he? Well the has one of the best arms in the game and he threw two last second Hail Marys in one season to send the game to overtime. Below is the first one, a last second pass to Richard Rodgers against the Detroit Lions.
To throw the football that far you need some serious arm strength and accuracy. In the pass he threw the ball 67 yards and the hang time was 4.1 seconds. With this in mind its possible to calculate the horizontal and vertical velocities. The horizontal velocity is vx = 60.26m/4.1s = 14.9m/s. The vertical velocity is v = gt/2 = 20.1 m/s. This gives an actual velocity of 25m/s or 90km/hr.
Next find the angle at which he threw the ball. From the above picture the angle I measured was 53 degrees. With all of this in mind now plug into kinematics equations to work out a graph of the height of the football and downfield distance.
From here its clear that Rodgers had to throw the football at a 53 degree angle, if he miscalculated the angle by just 5 degrees the ball would have landed just 63 yards downfield; four yards outside of the endzone. If he had thrown the football at 45 degrees to get maximum distance the ball would have travelled 70 yards down the field and ended up in the back of the endzone where no receivers were present. The kinetic energy of the pass was about 135J which is the same as a baseball pitcher's fastball going at 100mph.
But what if somehow Rodgers had magically ended up on the Moon as he was about to launch the football?
On the Moon the acceleration due to gravity is just 1/6th that on the Earth. If Rodgers threw the football with same force and angle the football would have ended up landing 410 yards away and reached a maximum height of 120 meters. So how good is Aaron Rodgers? Probably the best quarterback in the sport that can not only throw a football very far but also very accurately.
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