A hot-air balloon rises vertically so that its height (in meters) and the observer’s…

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

Problem

A hot-air balloon rises vertically so that its height

h

(in meters) and the observer’s angle of elevation

\theta

(in radians) satisfy

\tan\theta = \dfrac{h}{120}

. When

\theta = 0.5

rad, the angle is increasing at a rate of

0.03

rad/s. Determine

\dfrac{dh}{dt}

at that instant, including proper units.