# A searchlight rotates at a rate of 3 revolutions per minute. The beam hits a wall located 6 miles...

## Question:

A searchlight rotates at a rate of {eq}3{/eq} revolutions per minute. The beam hits a wall located {eq}6{/eq} 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 {eq}\Theta{/eq} between the beam and the line through the searchlight perpendicular to the wall is {eq}\frac{\pi }{5}{/eq}? Note that {eq}\frac{d\theta}{dt}=3(2i)=6\pi{/eq}.

## Related Rates:

Recall that the rate of change of an object is the rate at which it changes over time and is calculated as the derivative with respect to time. When two objects are related (like radius and area of a circle), then their rates of change will be related and if given the rate of one variable, we may be able to find the rate of change of the other.

Let {eq}y {/eq} be the distance between the searchlight and the spot on the wall where the beam is hitting. If {eq}\theta {/eq} is the angle made...

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