How to calculate angle for a rocket trying to hit another rocket

Question

I have a rocket A that has a constant velocity and a direction.

I have another rocket $B$ that has a constant velocity and a starting angle. I want to calculate the angle for the rocket $B$ so that with the calculated angle it would eventually hit the A rocket.

I realize the angle would be different at every moment. And thus I would recalculate it on every moment in the simulation.

Where would I even start? What are the common methods to look at?

Answer 1

The easy way of doing this is to draw a picture showing the initial positions, with a line, the "initial line" joining the two points. Now draw arrows from the endpoints so that the first rocket with speed $u$ makes angle $\alpha$ with the initial line. The second rocket has speed $v$ and makes unknown angle $\beta$ with the initial line.

Then the condition for interception is $$u\sin\alpha=v\sin\beta$$ from which you can calculate $\beta$

A nice pay-off is that you can also easily calculate the time to interception, if $d$ is the initial distance between them, as $$t=\frac{d}{u\cos\alpha+v\cos\beta}$$

Answer 2

The angle does not change. The relative velocity $v_{rel}= v_B-v_A$ vector is constant in direction and magnitude. Angle can be easily found as $A , v_{rel}$ are known in direction and magnitude.

Time for collision can be found as initial distance/ magnitude of relative velocity.