Uppose the human cannonball, David Marvin, wants to create a world record at the AT&T Stadium in Arlington, Tx while the jumbotron (gigantic tv) is down for repairs. He plans for his cannon to be set up near a goalpost such that when he exits the cannon, he will be directly above one goal crossbar, and he aims to field goal himself on the other side, ie fly between the uprights, in addition to reaching a substantial height in the stadium. Thus, he must adjust the angle and launch speed of his 8 m long cannon, which is currently capable of propelling him to a speed just shy of 75 mph (<-- this is true).

Stadium Notes: Stadium Height = 320. ft (1 ft. = 0.3048 m)

Field length = 120. yds (from goalpost to goalpost) (1 yd = 0.9144 m)

Suppose he is able to tweak his cannon such that it will propel him at a speed of 99.0 mph (1 mph = 0.447 m/s) at an angle of 73.0 degrees. Assuming his landing zone is a 2 m long x 2 m wide x 8 m deep box filled with foam at the far end of the field on the back side of the goal post, and using your knowledge of kinematics and projectile motion, determine whether his plan will be successful by performing the following calculations (imagining David as a cannonball):

1. Motion during launch, before flight:

(a) First, take a guess, will he make it (simple yes or no, no wrong answer, what do you think)?

(b) During launch, what will be the g-force David would experience (similar to in-class example)?

(c) What will be the duration of the launch (not the flight)?

(d) Using the image to the right, which depicts the potential limits of human tolerance as a function of acceleration (g-force), direction of g-force and duration, will he pass out at launch (yes/no/maybe)?
. For example, the blue curve is the max g-force for acceleration upward in the y-direction such that a person would likely pass out at a a sustained 12g for 0.3 s.

Hint: remember his launch angle is 73 degrees which is less than vertical (blue) and greater than 45 degrees (red) curves.

2. Motion during flight, after launch:

(a) How high will he fly?

(b) Analyze: Will he be launched into the roof (yes or no)?

(c) How far will he travel?

(d) Analyze: Will he fly farther than the goalpost (yes or no)?

(e) What will be his height at the crossbar (similar to in-class example)?

(f) Analyze: If the goalposts have regulation dimensions as shown below, Will he clear the cross bar which is at 10 ft high (yes or no)?

(g) Analyze: Will he fly between the top and bottom of the uprights (that is, in the 20 ft span above the crossbar)?

Football Goal Post Dimensions (h) Analyze: Will he land inside the landing zone?