(Solved): A searchlight rotates at a rate of 3 revolutions per minute. The beam hits a wall located 11 miles ...

A searchlight rotates at a rate of 3 revolutions per minute. The beam hits a wall located 11 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 \( \theta \) between the beam and the line through the searchlight perpendicular to the wall is \( \frac{\pi}{4} \) ? Note that \( d \theta / d t=3(2 \pi)=6 \pi \). Speed of dot \( = \) mph.