For an observer standing 40 m from the base of a vertical flagpole

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

Problem

For an observer standing 40 m from the base of a vertical flagpole, the angle of elevation

\theta

to the top of the pole changes as the pole is raised at a vertical speed of

v

meters per second. Which of the following expressions gives

\dfrac{d\theta}{dt}

in terms of

v

and

\theta

at that instant? (a)

\displaystyle \frac{v}{40}\tan\theta

(b)

\displaystyle \frac{v}{40}\sec^{2}\theta

(c)

\displaystyle \frac{v}{40}\cos^{2}\theta

(d)

\displaystyle \frac{v}{40}\cos\theta