A weather balloon rises vertically at while an observer walks directly toward the…

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

Problem

A weather balloon rises vertically at

3\text{ m/s}

while an observer walks directly toward the balloon at

1.5\text{ m/s}

along a straight level path. At a certain instant the observer is

45\text{ m}

horizontally from the point directly below the balloon, and the balloon is

80\text{ m}

above the ground. What is the rate of change of the angle of elevation

\theta

(in rad/s) at that instant? (a)

0.067\text{ rad/s}

(b)

0.016\text{ rad/s}

(c)

0.030\text{ rad/s}

(d)

0.040\text{ rad/s}