A Lighthouse Is Located on a Small Island $3 \mathrm {~km}$

A lighthouse is located on a small island, $3 \mathrm {~km}$ away from the nearest point $P$ on a straight shoreline, and its light makes four revolutions per minute. How fast is the beam of light moving along the shoreline when it is $1 \mathrm {~km}$ from $P$ ? Select the correct answer.

A) $1900 \pi \mathrm { km } / \mathrm { h }$
B) $2000 \pi \mathrm { km } / \mathrm { h }$
C) $1800 \pi \mathrm { km } / \mathrm { h }$
D) $1700 \pi \mathrm { km } / \mathrm { h }$
E) $1600 \pi \mathrm { km } / \mathrm { h }$