As the sun sets behind a 120-foot building, the building's shadow grows. How fast is the shadow growing (in feet per second) when the sun's ray make an angle of pi/3 radians?

Question

As the sun sets behind a 120-foot building, the building's shadow grows. How fast is the shadow growing (in feet per second) when the sun's ray make an angle of pi/3 radians?

Answer 1

Length L of shadow L = 120cotθ; dL/dt = - 120csc²θdθ/dt; dL/dt; dθ/dt = - 2π/86400 rad/s = - π/43200 rad/s;

dL/dt = 120csc²π/3·π/43200 feet/s = 0.0349 feet/s