Question

Suppose, you live in a place on the equator. There is a vertical rod of length 2m on
your roof top. One morning, you went to the roof top and observed the shadow of the
rod. If the length of the rod was 1m, then what time was that?

Answer 1

Answer on Question #50134, Physics, Mechanics | Kinematics | Dynamics

Suppose, you live in a place on the equator. There is a vertical rod of length $2\mathrm{m}$ on your roof top. One morning, you went to the roof top and observed the shadow of the rod. If the length of the rod was $1\mathrm{m}$ , then what time was that?

Solution:

On the Equator, the duration of daylight is not exactly 12 hours all the year round. At $0{}^{\circ}$ we have 6 a.m., at $90{}^{\circ} - 12$ p.m.

The altitude of the sun is

$$\alpha = \tan^ {- 1} \left(\frac {2}{1}\right) = 6 3. 4 3 {}^ {\circ}$$

The time is

$$t = 6 + \frac {6 3 . 4 3}{9 0} * 6 = 1 0. 2 3 \mathrm {a . m .} = 1 0: 1 4 \mathrm {a . m .}$$

Answer: 10: 14 a.m.

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