A searchlight rotates at a rate of 3 revolutions per minute. The beam hits a wall located 12 miles away and produces a dot of light that moves horizontally along the wall. How fast (in mph)...

Question

A searchlight rotates at a rate of 3 revolutions per minute. The beam hits a wall located 12 miles away and produces a dot of light that moves horizontally along the wall. How fast (in miles per hour) is this dot moving when the angle θ between the beam and the line through the searchlight perpendicular to the wall is π/5? Note that dθ/dt = 3(2π) = 6π.

Speed of dot =   mph. 

Answer 1

x = 12tanθ mi; dx/dt = 12sec²θdθ/dt = 12sec²(π/5)·6π mi/min = 345.5947 mi/min =20735.68 mi/h