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

×