Cadillac Mountain, elevation 1530 feet, is located in Acadia National Park, Maine, and is the highest peak on the east coast of the United States. It is said that a person standing on the summit will be the first person in the United States to see the rays of the rising Sun. How much sooner would a person atop Cadillac Mountain see the first rays than a person standing below, at sea level? [Hint: Consult the figure. When the person at $D$ sees the first rays of the Sun, the person at $P$ does not. The person at $P$ sees the first rays of the Sun only after Earth has rotated so that $P$ is at location $Q .$ Compute the length of the arc subtended by the central angle $\theta .$ Then use the fact that, at the latitude of Cadillac Mountain, in 24 hours a length of $2 \pi(2710) \approx 17027.4$ miles is subtended, and find the time that it takes to subtend this length.] (FIGURE CAN'T COPY).