A spotlight located on the ground from a vertical wall sweeps upward

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

Problem

A spotlight located on the ground

10\text{ m}

from a vertical wall sweeps upward, creating a spot of light that moves on the wall. If the beam makes an angle

\theta

with the ground and is rotating at

0.10\text{ rad/s}

, how fast is the spot moving when it is

4\text{ m}

above the ground? (a)

0.91\,\text{m/s}

(b)

0.40\,\text{m/s}

(c)

1.16\,\text{m/s}

(d)

1.08\,\text{m/s}