A submarine is descending vertically beneath a surface buoy attached by a 300 m cable

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

Problem

A submarine is descending vertically beneath a surface buoy attached by a 300 m cable. The cable makes an angle

\theta

with the vertical that satisfies

\theta = \arcsin\!\left(\dfrac{y}{300}\right)

, where

y

(in meters) is the submarine’s depth. When

y = 120\text{ m}

, the depth is increasing at

\dfrac{dy}{dt}=2\text{ m/s}

. Determine

\dfrac{d\theta}{dt}

at that moment.