Dr. Nestler's Math 7 Calculus 1

In the episode "Bart of Darkness" (1F22) of The Simpsons, Bart Simpson falls out of the treehouse in his backyard and breaks his leg.  It takes him approximately 5 seconds to hit the ground.

1.  Assume that Bart falls from rest (he does not jump), and the only force acting on him is the acceleration due to gravity which is 32 feet per second squared.  Write down and solve an initial value problem (differential equation and one or more initial conditions) that results in the height of the treehouse.

2.  Assume that consecutive floors of a building are separated by 12 vertical feet.  Approximately how many stories high is the treehouse?  Are you surprised that Bart only broke his leg?

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