A movie studio places a small mobile floodlight on a dolly that rolls horizontally…
MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A movie studio places a small mobile floodlight on a dolly that rolls horizontally along a track 3 m above ground level. The light moves parallel to the ground at a constant speed of 0.50 m/s and shines directly forward onto a stationary statue that is 2.0 m tall, casting a shadow on the ground in front of the statue.
At a certain instant, the light is 4.0 m horizontally behind the statue (measured along the track). Let y(t) be the horizontal distance from the light to the statue, and s(t) the length of the statue’s shadow on the ground.
(a) Determine the instantaneous rate at which the shadow length s is changing when y=4.0 m. Be sure to include units.
(b) At the same instant, compute the speed of the shadow’s tip relative to the ground and state its direction with respect to the statue.