An observer stands from a straight road

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

Problem

An observer stands

80\text{ m}

from a straight road. A car travels along the road at a constant speed of

25\text{ m/s}

. Let

\theta

be the angle between the observer’s line of sight and the perpendicular from the observer to the road. What is the magnitude of

\dfrac{d^{2}\theta}{dt^{2}}

(in rad/s

^{2}

) when the car is

100\text{ m}

from the point on the road closest to the observer? (a)

0.074

(b)

0.018

(c)

0.037

(d)

0.028