Mathematics > calculus > Application Of Derivatives

Case Study - 1

The traffic police has installed Over Speed Violation Detection (OSVD) system at various locations in a city. These cameras can capture a speeding vehicle from a distance of $300$ m and even function in the dark. A camera is installed on a pole at the height of $5$ m. It detects a car travelling away from the pole at the speed of $20$ m/s. At any point, $x$ m away from the base of the pole, the angle of elevation of the speed camera from the car $C$ is $\theta$.

(i) Express $\theta$ in terms of height of the camera installed on the pole and $x$.