For extra credit, this is what I'm up against (I have no intention of people solving the problem for me, and thus variable values have been removed). Good thing other students have gone before and I have only to read very carefully what they're doing and follow their directions...just not at 12:40 in the morning...as usual I'm afraid of what'll happen to me tomorrow with classes solid from 8 till 4 but ah well...
You are designing a missile defense system that will shoot down incoming missiles that pass over a perimeter defense post. The set-up is shown below. A missile passes directly above the base: radar at the base can measure the height, h, of the incoming missile and the speed of the missile, v1. Your patriot missile is set to fire at an angle of q = ??.? degrees from vertical. You design the missile so the magnitude of the acceleration is given by:
a2 = C e-bt
where
C can be set on the missile as it is fired, and
b = 0.?? s
-1. The direction of the
vector acceleration stays at the same angle,
θ, for the entire trip. If a missile passes over at a height of ?.?? km and a constant speed of ???.? m/s (this means that
v1 is constant), solve for C for that missile. You will also need to enter results from intermediate steps of your calculation, including the time
Dt in between launch and impact, and the horizontal distance
Dx from the launch station to the impact position.
