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When a model rocket is launched straight up with an angle of 90degrees to the ground it will do a 180 flip when it reaches the apex of its flight and then dive straight down to Earth.

If I were to launch a rocket at 0degrees to the ground it would fly straight and eventually angle down until the nose hits the ground.

At what angle does the rocket stop doing the 180degree flip and, instead, continue flying in a parabola until it reaches the ground?

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The flip is purely down to the aerodynamics of the rocket, which is (presumably) designed so the nose always points into the wind.

If you imagine launching the rocket at 45º then it will follow a parabola (ignoring slowing due to drag) with the nose pointing in the direction of motion. If you increase the angle to 89º then it still follows a parabola but the parabola is much narrower, and the rate the rocket flips over at the top much greater. As you increase the angle closer and closer to 90º the parabola gets narrower and narrower and the rocket turns over ever more rapidly at the top.

The point of all this is that the straight up and down flight at 90º is still a parabolic curve, but in the limit where the parabola has zero width. If we extrapolate from the wider parabolae then in the straight up and down flight the rocket would flip over infinitely quickly. Obviously in practice the air resistance and moment of inertia of the rocket means the flipover will take a finite time. How long it takes will depend on the design of the rocket.

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