$45$ A hawk flying at $\backslash (15\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ at an altitude of $180$ m accidentally drops its prey. The parabolic trajectory of the falling prey is described by the equation $\backslash [$ y$=180-\backslash$frac$\{$x$^\{2\}\}\{45\}\backslash ]$ until it hits the ground, where $\backslash ($ y $\backslash )$ is its height above the ground and $\backslash ($ x $\backslash )$ 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. Express your answer correct to the nearest tenth of a meter.