A camera is located 30 ,m from the base of a weather balloon

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

Problem

A camera is located 30\,m from the base of a weather balloon. The angle of elevation

\theta

(in radians) to the balloon satisfies

h=30\tan\theta

, where

h

is the balloon’s height (in meters). When

\theta=\dfrac{\pi}{4}

, the angle is increasing at a rate of 0.10\,rad/s. Determine the vertical velocity of the balloon at that instant, in m/s.