An airplane is at an altitude of and a horizontal distance of from an observer

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

An airplane is at an altitude of

3\text{ km}

and a horizontal distance of

7\text{ km}

from an observer. At that instant the plane is climbing at

8\text{ m/s}

and moving horizontally away from the observer at

150\text{ m/s}

. What is the rate of change of the angle of elevation

\theta

(in rad/s) from the observer to the plane at that moment? (a)

-9.5\times 10^{-3}

(b)

\phantom{-}6.8\times 10^{-3}

(c)

-6.8\times 10^{-3}

(d)

-8.0\times 10^{-3}