An observer stands from the point directly below a hot-air balloon that is rising at…

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

Problem

An observer stands

150\,\text{ft}

from the point directly below a hot-air balloon that is rising at a constant

10\,\text{ft/s}

. Let

\theta

be the angle between the observer’s line of sight to the balloon and the horizontal ground. Which statement best describes how

\theta

and its rate of change behave as the balloon ascends? (a)

\theta

increases, and

\dfrac{d\theta}{dt}

decreases over time. (b)

\theta

increases, and

\dfrac{d\theta}{dt}

remains constant over time. (c)

\theta

decreases, and

\dfrac{d\theta}{dt}

is negative. (d)

\theta

increases, and

\dfrac{d\theta}{dt}

increases over time.