## The Packer's Hail Mary

Down by two points with zero seconds left on the game clock, the Green Bay Packer’s quarterback, one of the top tier NFL quarterbacks of the year, Aaron Rodgers, unleashed a massive 67 yard Hail Mary pass from his own 36 yard line, which landed right in the hands of tight end Richard Rodgers. The play was controversial for Green Bay haters, as it came after a slightly questionable facemask call that gave the Packers another shot at the last down of the game. For Green Bay fans this controversy only added to the heroic allure of the play.

 Analysis of the angle of release of the ball shows that Rodgers threw the ball at a nearly 45 degree angle
When I first saw the play on Thursday night, my immediate reaction was to jump up and down screaming and pumping my fists, as any passionate sports fan would. It wasn’t until the next day, seeing the replays that I began to question the physics of the pass. As can be seen in this video, the ball is launched so high that it passes out of the camera frame before descending into Rodgers’ open arms. From another angle, it is clear that the balls parabolic arc take its very close to the stadiums ceiling. I began to question the massive strength it must take to throw the ball 61 yards, and how the physics of projectile motion apply to football. Using a time measurements from the game footage and pictures of the pass to determine the angle of release, the maximum height the ball reaches can be calculated. Knowledge of the physics of projectile motion, the internet, and a protractor were the only tools necessary.

Δx= 67.0 yards (61.26m)
t= 4.35 seconds
Θ= 45°
V0=14.1 m/s
g= -9.8 m/s2

Vy0= Vo sinΘ
Vy0= 9.95 m/s

If we set the height that Aaron Rodgers released the ball from equal to zero and the time it took to reach the peak equal to half of the total travel time, solving for the final height of the ball becomes very simple.

y= y0 + vy0 - .5gt2

y= 33.1 m

1 meter= 3.28 feet

The ball peaked 109 feet above the point where Aaron Rodgers released the ball.