The height (in meters) of a pendulum bob above its lowest point is related to the…

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

The height

y

(in meters) of a pendulum bob above its lowest point is related to the angle

\theta

(in radians) the pendulum makes with the vertical by

y = L - L\cos\theta

, where the pendulum’s length is

L = 2.0\,\text{m}

. At the moment when

\theta = \dfrac{\pi}{6}

and the bob is moving upward at

\dfrac{dy}{dt}=0.35\,\text{m\!/s}

, determine the bob’s angular speed

\dfrac{d\theta}{dt}

(include units and sign).