Calculating Line of Sight and Obstruction in Restaurant Redesign

[swopidopi]

I'm working on re-designing a restaurant by the sea. I'm a interior decorator so I know very litle about physics. Here's my question:

let's say you're in the back of a room with 90 meters of floor in front of you. You are 7 meters above ground but your eyes are only 10 cm above the floor. I've calculated that 7.1 meter up with a clear view gives you a line of sight of 9.6 km. Will i be able to see the horizon with the floor infront of me and if yes; how much of my line of sight will be obstructed by the floor. I've drawn a picture so you can understand the question better.

Thank you.

 

[gneill]

Hi swopidopi, Welcome to Physics Forums.

Please remember to use the template provided to format your homework help requests.

Your problem is not so much a physics problem as an exercise in math/geometry. It boils down to determining where (or if?) a ray originating at the observer's eye and just grazing the outer edge of the platform intersects curved surface of the Earth. You should be able to write equations for both the circle represent the Earth's surface and the line which incorporates the ray.

I'm working on re-designing a restaurant by the sea. I'm a interior decorator so I know very litle about physics.

A restaurant whose customers lie on the floor at the back of the room? One hopes that this but a passing fad.

 

[haruspex]

Based on the text, I shall assume this is not homework.
From the eye to the far edge of the floor, the line of sight drops .1m in 90m, or 1 in 900.
From there to the horizon, it drops 7m in 9600m, or 1 in 1370. So that settles whether the horizon will be visible.
As to how much of the view is lost, it depends how you measure it. Say it is in terms of optical angle. If you were to stand at the edge of the drop you would see 90 degrees, from vertically down to horizontal. From the given viewing height of 0.1m from the back edge, you will see less than one tenth of a degree. But I would think customers that drunk won't care.

 

[TSny]

From there to the horizon, it drops 7m in 9600m, or 1 in 1370.

Does this take into account the curvature of the earth? I get that the line of sight to the horizon would drop more than this, about 1 in 670.

 

[haruspex]

Does this take into account the curvature of the earth? I get that the line of sight to the horizon would drop more than this, about 1 in 670.

That's true, but I was not expecting it to make that much difference. Thanks for checking that.