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Q: Find the maximum angle a projectile can be shot so that it's distance from the origin is always increasing. Air resistance negleced.

So there is the x and y position based on initial velocity, angle, and time, but I made initial velocity equal 1 for simplicity. Next, make a vector out of this and find the distance of the vector at varying angle and time.

Take the time derivative and make sure it is never negative. Unfortunately, there is no angle where change in the projectile's distance is zero at the point where it lands, so I can not make the whole equation all in terms of the angle.

So what can I do?

I'm pretty damn sure the answer is ~70.356 deg.