Delivery Drone

Calculus Level 2

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 \(\displaystyle \int \sqrt{a^2+u^2}\,du=\frac{u}{2}\sqrt{a^2+u^2}+\frac{a^2}{2}\ln(u+\sqrt{a^2+u^2})+C.\)

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