Calculating Projectile Trajectories in 3D Space: Applying Physics and Calculus

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To hit a moving target in 3D space, one must calculate the projectile's trajectory based on the enemy ship's constant velocity and the missile's speed. The key is to derive equations that describe both the projectile's path and the ship's path in terms of time. This involves using parametric equations to represent the motion of both objects. By equating their positions at a specific time, one can determine the necessary launch angle for the missile. Understanding the underlying physics principles and equations is crucial for solving this problem effectively.
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Forgive me if this is deemed a "homework question", b/c it kinda is, but I'm thinking about it a little differently...

It's a 3 dimensional calc. III problem, that I've broken down to this: Essentially there's an "enemy ship" traveling in a straight line at a constant velocity. I'm stationed at the origin and I want to fire at the ship (I know the speed the missle will fire at). So how do I determine at what angle to fire the missle so that it hits the moving target? I know it really boils down to a simple physics equation that I should remember from a million years ago..but, I don't... HELP! :bugeye:
 
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it is a time problem, find equations in terms of time which describe the path taken by the projectile and one which describes the ships path. Find the point they arrive at at the same time.
 
Exactly...how do I find these time equations? Would they be parametric? Would they be based off of some simple physics equations that I'm just missing?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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