Projectiles aren't as easy as you might think

Classical Mechanics Level 4

A ball is thrown from ground With a velocity \(v_{0}\), and at an angle \(\theta\). With what angle \(\theta\) should the ball be thrown to give it maximum arc length or maximum distance for its trajectory to cover? If \(\theta\) is the maximum value find:

\[\left\lfloor \theta \right\rfloor\] in degree?

Details and Assumptions

Maximum range doesn't necessarily mean maximum arc length.

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