Tiffany is a model rocket enthusiast. She has been working on apressurized rocket filled with nitrous oxide. According to herdesign, if the atmospheric pressure exerted on the rocket is lessthan 10 pounds/sq.in., the nitrous oxide chamber inside the rocketwill explode. Tiff worked from a formula p=14.7e?h/10p=14.7e?h/10pounds/sq.in. for the atmospheric pressure hh miles above sealevel. Assume that the rocket is launched at an angle of ?? abovelevel ground at sea level with an initial speed of 1400 feet/sec.Also, assume the height (in feet) of the rocket at time tt secondsis given by the equationy(t)=?16t2+1400sin(?)ty(t)=?16t2+1400sin?(?)t. [UW]
a. At what altitude will the rocket explode?
b. If the angle of launch is ?? = 12??, determine the minimumatmospheric pressure exerted on the rocket during its flight. Willthe rocket explode in midair?
c. If the angle of launch is ?? = 82??, determine the minimumatmospheric pressure exerted on the rocket during its flight. Willthe rocket explode in midair?
d. Find the largest launch angle ?? so that the rocket will notexplode.
