A tracking station is located from the vertical launch pad of a rocket

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

Problem

A tracking station is located

1000\text{ m}

from the vertical launch pad of a rocket. At the instant the rocket is

600\text{ m}

above the ground, its upward velocity is

80\text{ m/s}

. Assuming the rocket moves straight up, what is the camera’s angular speed

d\theta/dt

(in rad/s) at that instant, where

\theta

is the angle between the ground and the line of sight to the rocket? (a)

0.080\text{ rad/s}

(b)

0.109\text{ rad/s}

(c)

0.059\text{ rad/s}

(d)

0.069\text{ rad/s}