Confusing projectile motion problem?

[bronxbomber91]

Homework Statement

You are designing software for an anti-aircraft system. Your guns have a maximum horizontal range R, and can be fired at any angle (call it "A") above the horizontal. Enemy aircraft are spotted at time t=0, flying at altitude H, distance D, horizontal velocity V toward a point directly above your guns. You are a physicist who understands projectile motion, and what it means to "hit" a target. The following questions explore how you figure out when and in what direction to fire the guns.

a) Make a labeled sketch of the graph (already done)
b) What is the highest H your gun can reach?
c) Write the two equations for the height and horizontal distance of the plane from the guns as a function of time, t, since the time (t=0) it was sighted.
d) Should you program the guns to fire as soon as the plane is sighted? Or should you calculate when to fire and at what angle to the horizontal?
e) In the case the plane is flying low enough that your guns can hit the plane at some angle, at what angle should they be fired to hit it at the highest point of the shell's trajectory?
f) How soon after sighting should they be fired?

Homework Equations

The Attempt at a Solution

a) Our teacher said that our group's sketch was fine so that isn't a problem.

b) My guess was H = -(initial velocity)^2/2g, but I have a feeling that's incorrect.

c) For height, I put H(t) = H, because isn't the plane's altitude constant? For horizontal distance, I put D(t) = D - Vt. This equation is the only one i have any confidence in.

d,e,f) Honestly I'm completely stumped, as was the rest of my class. Any help would be greatly appreciated.

 

[redargon]

ok, for b) you're almost correct, but does a negative answer make sense? what would cancel out that negative?

I think you answer for c) makes sense.

d) if we think about it, if the plane altitude is the same as the guns maximum height, then you could only hit the plane when it was directly overhead. but you'd have to fire at a time slightly before the plane got to that position, to take into account the time the bullet takes to get to that position. There hasn't been any mention of bullet speed, but we could just call it Vinitial, as you did for b).

that's about as much as i got for you for the moment.