Please EXPLAINNairobi and Rio are located on the Tropic of C

Please EXPLAIN.....Nairobi and Rio are located on the Tropic of Capricorn. On December 21, that is on the day of the Solstice at midday the Sun is vertical. How fast is the shadow of a pole 3 meters tall increasing at (a) midday, (b) at dusk?

Solution

When the sun is vertically overhead along the Tropic of Capricorn at mid-day---

a). Days and nights are of equal length in the Northern Hemisphere.

b). Nights are longer than days in the Southern Hemisphere

c). Day and nights are of equal length at the poles.

d). Night is equal to 24 hours of the North pole.

Hence at midday, the Sun is vertical the shadow will not be shown and increase rate is 0

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At dusk almost angle will be nearing 90 degrees. Hence shadow will increase at the fastest rate equal to 1.