# A simple query on sun's speed

1. Jul 22, 2011

### alankar

Hi,

I have a peculiar query, including theories of light, Sun's speed and movement. Following is the query :

Imagine there is a hill like a half circle and sun is rising on a side of hill, on the opposite side there is a person standing waiting to see sun, as sun moves up in the sky. The hill's arc (half circle's perimeter) is 4KM. Could there be any calculation so that we know after sun rise how much time it would take so that Sun could be seen by the person standing on the other side of hill?

Waiting for any kind of help in this, Thanks in advance for your replies.

Thanks,
Alankar

2. Jul 22, 2011

### phinds

I'm confident it can be worked out mathematically, but only if you give enough information for there to be a solution.

How far along are you in math? You have left out some very fundamental factors.

For example:

(1) How far are the person's eyes from the ground?
(2) How far away from the hill is the person standing?

3. Jul 22, 2011

### Jack21222

You would probably also need to know the latitude and what time of year, to know the sun's path across the sky. If it's an antarctic winter, the answer could be months, to give one extreme.

4. Jul 22, 2011

### marcus

You have not said how tall the person is---how high his eyes are, from the ground.

If he is as big as an ant, so his eyes are right at ground level, and if he is right at place where the semicircular arc of the hill comes down to the flat ground, then he will be in shadow for a long time---perhaps until nearly noon. For an ant right next to the hill, the hill makes a big shadow.

A semicircle arc, where it meets the flat level, is almost vertical. It looks like a huge vertical wall to the ant, and he is right next to the base of the wall. So the size of the person matters.

Also keep in mind that the sun does not always appear to rise straight up from the horizon. At different times of year it can seem to rise and set along a slanted path.

To solve the problem, you might consider making simplifying assumptions.

Like for example suppose the man is 2 meters tall . Then his height is 1/2000 of the length of the hill's arc, which you say is 4000 meters. Say that it is the Spring Equinox and the man lives on the Equator, like in Singapore. So then the sun will rise straight up perpendicular from the horizon and it will rise 90 degrees in the first 6 hours of the day----so it will rise 15 degrees each hour. It takes 4 minutes to move 1 degree.

If this is a homework problem, for school, then you should go to the homework section of Physicsforums.

They will probably suggest that you make explicit some simplifying assumptions, like what I suggested. Then, with those assumptions, you will learn how to solve the problem.

===================

EDIT: After posting this, I saw that PHinds and Jack had already covered all or most of the points here. Didn't see your posts. Sorry about simply repeating.

Last edited: Jul 22, 2011
5. Jul 22, 2011

### marcus

I will show you what comes of the simplifying assumptions that I mentioned. If the man is 2 meters tall (or his eyes are 2 meters off the ground) and he stands right next to the base of the hill, what angle does he make? One quadrant, 90 degrees, of the arc of the hill is 2000 meters. His height is 1/1000 of that.

I think his height represents 90 degrees divided by 1000. That is 9/100 of one degree.
His line of sight, looking up the side of the hill, must be nearly vertical, but not quite vertical. It must be slanted from vertical by 9/100 of one degree to the east.

That comes of assuming that his eyelevel height is 2 meters. You would want to make some more realistic assumption, but that gives a sample of what can be expected.

6. Jul 22, 2011

### phinds

Hm ... wonder why I didn't think of that.

7. Jul 22, 2011

### marcus

Obviously you did think of it
I took a long time writing my post and did not see that two other people had responded before me. You and the other poster raised all the points before I did.

Maybe I should edit my post to acknowledge.

Last edited: Jul 22, 2011
8. Jul 22, 2011

### phinds

Marcus you make so many posts here that it amazes me that you EVER have time to read previous posts in the threads. I was just having some fun at your expense.

Thanks for all the effort you put in here. Very helpful to newbies such as me.

9. Jul 23, 2011

### alankar

Hi !

Thanks for replies and further queries. I am assuming following :

1) The person's eye is at ground (neglecting his height).
2) The person's eye is at 180 cm above the ground.
3) The person is just touching the semi-circle arc.
4) The day, I am assuming is 23rd of March.
5) Person is at equator (0 degree Latitude) and 0 degree Longitude. (Whether possible or not).
6) The person is looking towards the hill (top of it).
7) If the arc is reduced to 3KM than what would be the change in time?

The question I am asking is not for any kind of school curriculum. I am doing some research work and for that I am looking for help. If there is any other more suitable forum then please tell me.

I hope I'll get some satisfactory resolutions now.

Thanks everyone.

Alankar

Last edited: Jul 23, 2011
10. Jul 23, 2011

### phinds

Still, given one of those, I think you have now specifed enough information that it can be worked out mathematically.

If you are expecting someone here to actually DO the math for you, you're likely to be disappointed. If you want an actual numerical answer, then start working on it and ask questinos if/when you get stuck.

11. Jul 23, 2011

### alankar

Hi,

I was writing item 1,2 and 7 as different situations.

Phinds, if I would know how to do the calculation, I was not asking a question here. This is not due to my laziness, but I don't know how to solve it. Anyway, if this is the last word then could anyone please direct me to a suitable forum?

Thanks for at least looking into it.

Alankar