You have entered a model rocket contest with yourfriend, Tiffany. You have been working on a pressurized rocketfilled with nitrous oxide. Tiffany has determined the minimumatmospheric pressure at which the rocket fuel is stable. Based nothat value, and the equations given below, your task is to determinethe optimum launch angle and initial velocity to maximize flighttime. The goal is to re-use your rocket capsule, so you really wantto avoid a fuel explosion.
The atmospheric pressure varies with elevation accordingto the equation: P(h)= 14.7e?h/10. where p is the pressure in psiand h, is an elevation in miles above sea levels. The height (infeet) of a rocket launched at an angle ? degrees with thehorizontal and an initial velocity, vo in feet/second, t secondsafter launch is given by the equationh(t)=-16t^2+vo*t*sin(?).
1) If Tiffany has determined that the minimum safepressure is 11 pounds per square inch, at what altitude will therocket explode? Report your result in feet. Round to the nearestfoot.
2) If the angle of launch is33o, with an initialvelocity of 1,648 what is the minimum atmospheric pressure exertedon the rocket during its flight? Report your answer to one decimalplace. Under these conditions, will the rocket explode during itsflight?
3) If the angle of launch is32o, with an initialvelocity of 1,908 what is the minimum atmospheric pressure exertedon the rocket during its flight? Report your answer to one decimalplace. Under these conditions, will the rocket explode during itsflight?
4) Tiffany has revisited her calculation and has nowconcluded that the minimum safe pressure for the fuel is 9 psi.What is the maximum height your rocket can achieve withoutexploding in flight? Report your answer in feet to the nearestfoot.
5) Tiffany has (once again) checked her calculations,and you have verified with her that the safe pressure for your fuelis 9 and the fuel capsule holds enough fuel to produce an initialvelocity of 2,169 feet per second. What launch angle will you useso that your rocket achieves the maximum safe altitude? Round youranswer to the nearest tenth of a degree.
