Niles lives at the top of a 1,000 ft tall tower in Singapore?

Question

...which can be assumed to be right on the equator. How much more daylight does he get than Miles who lives at the bottom?

Answer 1

OK assuming the base of the tower is at sea level.

Distance to horizon at sea level = approx 3 miles.

Distance to horizon at 1000 feet = 38.7 miles.

The circumference of the earth at the equator is 24,902 miles.

24 hours to revolve once. Speed of rotation 1037.58mph

The equator always has 12 hours sunlight and 12 hours dark each day.  The equator is the only great circle perpendicular to the earth’s axis of rotation.  No matter what time of year, the great circle of the equator will bisect the great circle of the sun’s illumination (think of a half moon)- so it will always remain half in the circle of illumination and half out- 12 hours each.

Now, deducting 3 miles from 38.7 and multiplying by two = 71.4 miles

24902 divided by 2 = 12451 miles in sunlight at any one time.

12451 divided by 12 = 1037.58 miles/hour change in area covered by sunlight.

71.4 divided by 1037.58 = 0.0688 hours or 4.128 minutes approximately.

Sorry if that was long winded. I was thinking it through as I was doing it.

Answer 2

Assume it's a simple geometry question .. you can assume the sun is a point source at  infinity (should make the calculations easier :-) ) and ignore diffraction through the atmosphere ..

PS don't forget the sun 'rises' for him early (as well as 'setting' late)