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?
+33665 The diagram below gives a simple representation:
The angle, θ = cos-1(R/(R+h)) where R is radius of the Earth (≈ 2.09*107 ft) and h = 1530ft
The Earth does a complete revolution (2pi) in 24 hours, so the time difference here is given by:
24hrs*θ/2pi or 24*60mins*θ/360 (with angles in degrees)
$${\frac{{\mathtt{24}}{\mathtt{\,\times\,}}{\mathtt{60}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{2.09}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{7}}}}{\left({\mathtt{2.09}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{7}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1\,530}}\right)}}\right)}}{{\mathtt{360}}}} = {\mathtt{2.773\: \!045\: \!192\: \!268}}$$
time difference ≈ 2.8 minutes
.
+33665 The diagram below gives a simple representation:
The angle, θ = cos-1(R/(R+h)) where R is radius of the Earth (≈ 2.09*107 ft) and h = 1530ft
The Earth does a complete revolution (2pi) in 24 hours, so the time difference here is given by:
24hrs*θ/2pi or 24*60mins*θ/360 (with angles in degrees)
$${\frac{{\mathtt{24}}{\mathtt{\,\times\,}}{\mathtt{60}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}^{\!\!\mathtt{-1}}{\left({\frac{{\mathtt{2.09}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{7}}}}{\left({\mathtt{2.09}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{7}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1\,530}}\right)}}\right)}}{{\mathtt{360}}}} = {\mathtt{2.773\: \!045\: \!192\: \!268}}$$
time difference ≈ 2.8 minutes
.
