A hawk flying at $12$m/s at an altitude of $183$ m accidentally drops its prey. The parabolic trajectory of the falling prey is described by the equation $$y=183 -\frac{x^2}{36}$$ until it hits the ground, where $y$ is its height above the ground and $x$ is the horizontal distance traveled in meters. Calculate the distance traveled by the prey from the time it is dropped until the time it hits the ground.

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