A searchlight rotates at a rate of 4 revolutions per minute. A straight road leads from the searchlight to a wall 7 miles away, perpendicular to the wall. The searchlight beam hits the wall and produces a dot of light that moves along the wall. How fast (in miles per hour) is this dot moving when the angle $$ heta $$ between the beam and the road is $$ \frac{\pi}{3} $$ ? Note that $$ d heta / d t=4(2 \pi)=8 \pi $$. Velocity of dot =

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A searchlight rotates at a rate of 4 revolutions per minute. A straight road leads from the searchlight to a wall 7 miles away, perpendicular to the wall. The searchlight beam hits the wall and produces a dot of light that moves along the wall. How fast (in miles per hour) is this dot moving when the angle $$ 	heta $$ between the beam and the road is $$ \frac{\pi}{3} $$ ? Note that $$ d 	heta / d t=4(2 \pi)=8 \pi $$. Velocity of dot =

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The speed of the dot of light is approximately $$ 13440\pi $$ miles per hour, or about 42281.6 miles per hour.

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