The interception of a plane problem

[Falkred]

You have a Surface to Air Missile System, SAM system for short, Your missile can travel at Mach 3.5 (2685.44 MPH) The system can rotate the missile before launch horizontally 30 Degrees per second and vertically at 15 degrees per second the rotation axis can rotate together to save on time. A aircraft that is identified as hostile aircraft is flying 13 miles due North of your System 3 miles above the surface at Mach .75 (575.5 MPH) heading East. You must take down this craft. Can your missile hit the aircraft? If so how long will it take to hit the aircraft? How far will the missile have to travel before striking the craft? how many degrees horizontally should the system rotate the missile before launching? how many degrees vertically should the system rotate the missile before launching? How long will it take to reach the degrees of optimal Launch?

I thought about this problem and have tried using google sheets and i have gone through Calculus A and am heading to Calculus B and i thought this problem up and am wondering if there is something from Cal A that i should be using for this? I do NOT want the answer i want the method or formula i should use. Thank you for looking at this and i look forward to talking with you.

-Falkred

 

[tkhunny]

Have you considered that there may be more solutions than just one

 

[Falkred]

Have you considered that there may be more solutions than just one

oh i know there are several like you could rotate ahead to where the plane will be and wait or you could cut it close or mix of the two but to mathematically do this is extremely tedious and very barbaric feeling so i am wondering if there is a method that i am missing. I appreciate you responding by the way!

 

[HallsofIvy]

The problem talks about the time it takes to "rotate" the missile horizontally and vertically but it does not appear to say what the initial position of the missile is! Are we to assume the missile is initiallly lying horizontal and pointing due north?

 

[Falkred]

The problem talks about the time it takes to "rotate" the missile horizontally and vertically but it does not appear to say what the initial position of the missile is! Are we to assume the missile is initiallly lying horizontal and pointing due north?

Yes sorry it is facing due north level with the ground

 

[tkhunny]

oh i know there are several like you could rotate ahead to where the plane will be and wait or you could cut it close or mix of the two but to mathematically do this is extremely tedious and very barbaric feeling so i am wondering if there is a method that i am missing. I appreciate you responding by the way!

When did calculus tend toward "barbaric"? It's a geometry problem if you don't find all solutions and let the calculus help you find the minimum (distance, time, other measures) solution.