Tiffany is a model rocket enthusiast. She has been working on a pressurized rocket filled with nitrous oxide. According to her design, if the atmospheric pressure exerted
on the rocket is less than 10 pounds/sq. in., the nitrous oxide chamber inside the rocket
will explode. Tiff worked from a formula
/10 14.7 h
p e


pounds/sq. in. for the
atmospheric pressure h miles above sea level. Assume that the rocket is launched at
an angle of α above level ground at sea level with an initial speed of 1400 feet/sec.
Also, assume the height (in feet) of the rocket at time t seconds is given by the
equation
   
2
y t t t    16 1400sin  . [UW]
a. At what altitude will the rocket explode?
b. If the angle of launch is α = 12°, determine the minimum atmospheric pressure
exerted on the rocket during its flight. Will the rocket explode in midair?
c. If the angle of launch is α = 82°, determine the minimum atmospheric pressure
exerted on the rocket during its flight. Will the rocket explode in midair?
d. Find the largest launch angle α so that the rocket will not explode.