The line of sight of the observer is tangent to the surface of the earth. This line of sight is thus perpendicular to the radius of the earth drawn to the observer's position. Complete the right triangle with the top of the mushroom cloud and we have:
Leg 1 = r
Leg 2 = distance from observer to top of mushroom cloud
Hypotenuse = r + 45,000 ft.
Where r is the radius of the earth, about 20,925,525 ft. Using the Pythagorean theorem, the distance from observer to mushroom cloud is about 1,373,070 feet, or 260 miles.What is the maximum distance a 45,000 ft mushroom cloud would be visible from?
i think you couldn't see anything farther than 10 kilometers or 6 milesWhat is the maximum distance a 45,000 ft mushroom cloud would be visible from?
i am assuming you try to say the mushroom cloud of atomic explosion? should be the distance from the Goraud of explosion to the Maximo high it can go
You need to construct yourself a right triangle. Place yourself on a circle (say the circumference of the earth.) Let's assume you're in the middle of the ocean and your eyes are just above water. (If you want to get picky don't forget to adjust for your own height.) As you look out in a straight line to the horizon (we'll call that a tangent line) you can see the curvature of the earth. Assuming you can see forever in a straight line, anything you can see must rise up to at least the level of that tangent line. The max distance will be found when that thing just touches that tangent line. I'd Use 4000 miles for the radius of the earth (I'd also state that I was doing that on my homework) and call your hypotenuse 4000miles + 45,000 feet. One adjacent side would be 4000 miles + the distance to your eyes. (Probably pretty safe to round this down to 4000 miles.) Then just apply the Pythagorean theorem.
Ain't math fun?
No comments:
Post a Comment