2) where is the sun located in the sky when the shadow is shortest?
3) At what time are the shadow longest during the day?
4)At what time are the shadow shortest during the day?
5)In which directions, the shadow of the pole falls at different times of the day?
6)Why does the length and direction of shadow keep on changing at different times?
Answers
theshadow is shortest when the sun is highest. That happens at solar noon wherever you are. Solar noon is often close to local noon, but is usually not exactly at the same time.
For instance, if you’re on the Greenwich Meridian (eg standing at the Royal Observatory in Greenwich, London) then solar noon is at exactly 12:00 UTC (because that’s essentially how UTC is defined).
How high the sun is at that time will depend on your latitude and the time of year. At the tropics, the sun is directly overhead at the Summer Solstice - that’s how the tropics are defined. North of the Tropic of Cancer, the sun will always be south of directly overhead. The further north you are, the further south it will be.
In fact, the relationship between the height of the sun at noon and latitude has been used as a navigational aid for a very long time. It’s possible to tell how far north/south you are by just observing the sun with a way of measuring its angle above the horizon (eg a sextant). You don’t need to know the time to do this (but you do need to know the rough date). To find out how far east/west you are, you need some way of measuring time reasonably accurately (eg compare the time of local noon with UTC noon, and you can easily calculate how far east/west you are)