The Sun’s rays make a constant angle of elevation with the horizontal

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

Problem

The Sun’s rays make a constant

60^{\circ}

angle of elevation with the horizontal. A hot-air balloon rises vertically at

4\text{ m/s}

from a point on level ground. When the balloon is

90\text{ m}

above the ground, how fast is the tip of its shadow moving along the ground? (a)

4\sqrt{3}\text{ m/s}

(b)

2\sqrt{3}\text{ m/s}

(c)

\dfrac{4}{\sqrt{3}}\text{ m/s}

(d)

4\text{ m/s}