A spotlight is positioned 2 ,m from a vertical wall and rotates in a horizontal plane…
MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A spotlight is positioned 2\,m from a vertical wall and rotates in a horizontal plane so that its beam makes an angle θ (in radians) with the perpendicular to the wall. At the moment when the beam strikes a point 4\,m above the floor, the illuminated point is moving upward along the wall at 3\,m/s. What is the instantaneous angular speed dtdθ of the spotlight (in rad/s)?
(a) 0.60
(b) 0.30
(c) 1.50
(d) 0.15