A hot-air balloon rises vertically at a constant rate of

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

Problem

4\text{ m/s}

. An observer stands on level ground

50\text{ m}

from the point on the ground directly beneath the balloon. When the balloon is

120\text{ m}

above the ground, what is the rate of change of the observer’s angle of elevation

\theta

(in rad/s)? (a)

0.0308

(b)

0.5408

(c)

0.0118

(d)

0.0800