Question $3$: A lighthouse is located on a mound of rock out in the ocean $2$ km from the nearest point $A$ on a straight shoreline. If the lamp rotates at a rate of $3$ revolutions per minute, how fast is the lighted spot P on the shoreline moving along the shorelline when it is $4$ km from point A $?$ Draw a sketch for the problem and solve it$.$

your work. $(10$ pts$)$ Show your work. $(10$ pts$)$