Imagine that you are a technical advisor to the Dave Letterman Show.
Your task is to design a circus stunt in which Super Dave Osbourne, who
weighs 170 pounds, is shot out of a cannon that is elevated 40 degrees
from the horizontal. The "cannon" is actually a 3-foot diameter tube that
uses a stiff spring and a puff of smoke rather than an explosive to launch
Super Dave. According to the manufacturer, the spring constant of the cannon
is 1800 N/m. The spring is compressed by a motor until its free end is
level with the bottom of the cannon tube, which is 5 feet above the ground.
A small seat is attached to the free end of the spring for Super Dave to
sit on. When the spring is released, it extends 9 feet up the tube. Neither
the seat nor the chair touch the sides of the 12-foot long tube. After
a drum roll, the spring is released and Super Dave will fly through the
air amidst sound effects and smoke. There is a giant airbag 3-feet thick
and 10 feet in diameter for Super Dave to land on. Where should this airbag
be placed for Super Dave to have a safe landing?