A diver is connected to a floating buoy by a 25 m rope

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

Problem

A diver is connected to a floating buoy by a 25 m rope. The rope makes an angle

\theta

with the vertical, modeled by

\theta = \arccos\!\left(\dfrac{d}{25}\right)

, where

d

(in meters) is the diver’s depth below the buoy. When

d = 15\text{ m}

, the diver descends at

\dfrac{dd}{dt}=0.30\text{ m/s}

. Compute

\dfrac{d\theta}{dt}

at that moment.