A delivery drone flying at constant speed $15 \text{ m/s}$ and constant height $2700 \text{ m}$ toward a destination drops its goods. If the trajectory of the falling goods until it hits the ground can be described by the equation $y=2700-\frac{x^2}{75},$ where $x$ is the horizontal distance it travels and $y$ is its height above the ground, what is the distance (not horizontal displacement) traveled by the goods until it hits the ground?

Note: You can use $\displaystyle \int \sqrt{a^2+u^2}\,du=\frac{u}{2}\sqrt{a^2+u^2}+\frac{a^2}{2}\ln(u+\sqrt{a^2+u^2})+C.$