A balloon ascends vertically from a point that is from a tracking camera at ground level

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

Problem

A balloon ascends vertically from a point that is

400\text{ m}

from a tracking camera at ground level. Its height (in meters) after

t

seconds is given by

h(t)=200t-3t^{2}.

Let

\theta(t)

be the angle between the ground and the camera’s line of sight to the balloon. What is the angular acceleration

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

(in rad/s

^{2}

) at

t=20\text{ s}

? (a)

-3.0\times10^{-4}\text{ rad/s}^{2}

(b)

-5.2\times10^{-4}\text{ rad/s}^{2}

(c)

\;5.2\times10^{-4}\text{ rad/s}^{2}

(d)

-1.5\times10^{-2}\text{ rad/s}^{2}