A camera is mounted on a tripod from a straight road

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A camera is mounted on a tripod

50\,\text{m}

from a straight road. A car travels along the road so that its distance

x(t)

(in meters) from the point on the road closest to the camera is given by

x(t)=20+15t+0.4t^2

, where

t

is measured in seconds. Determine the camera’s instantaneous angular speed

\frac{d\theta}{dt}

(in

\text{rad/s}

) when

t=5\,\text{s}