How much higher?

[dogdayz]

Imagine you constructed a hiking trail across the country. It is perfectly straight and flat, the total distance is 4000 miles.

You also installed a metal handrail along the trail.

An engineer comes along and tells you that in the summer the metal rail will expand increasing its length by one inch in total.

You think one inch over 4000 miles is no big deal but the engineer says no one will be able to reach the handrail.

Assuming the rail will buckle upward at the very centre how much higher from level will the handrail deflect?

[dogdayz]

No mathematicians out there.... I was sure somebody would come up with the answer.

[TLG]

No mathematicians out there.... I was sure somebody would come up with the answer.

I like a good challenge

Let's see ..... The way it reads , it's buckling upwards by 1 inch at the center creating a triangle

4000 miles in total = 2,000 miles at the centre or about 126.7 million inches

Using my handy dandy Pythagorean calculator --- (I'm cheating cause the pork chops are on the BBQ) where a2 + b2 = c2 to solve for h
So .... 127,000,000² + h² = 127,000,000.5²

Therefore for h we get ---- h = --------- hold i'll be right back ,, got to turn the chops

[dishuser]

I like a good challenge

Let's see ..... The way it reads , it's buckling upwards by 1 inch at the center creating a triangle

4000 miles in total = 2,000 miles at the centre or about 126.7 million inches

Using my handy dandy Pythagorean calculator --- (I'm cheating cause the pork chops are on the BBQ) where a2 + b2 = c2 to solve for h
So .... 127,000,000² + h² = 127,000,000.5²

Therefore for h we get ---- h = --------- hold i'll be right back ,, got to turn the chops

you found the same link on google as me...lol

[TLG]

you found the same link on google as me...lol

lol .... So what the answer then ?

[dishuser]

lol .... So what the answer then ?

11,260 inches, or 938 feet

[TLG]

LOL .... yes,, correct but !! That would be right if the earth was flat

4000 mi!es is a great distance and while that is the correct answer ,, it doesn't take into account the earth's curvature ....

So !! ,, The earth's circumference is approx 25,000 miles
And so 4000 miles represents about 6.25% of bend height

And so, using my handy dandy Pythagorean calculator we need to calculate the added hight .....

Ooooops got to turn those chops again ... LOL

[dishuser]

those chops are gonna taste flat...lol

[TLG]

lolololololllll !!

[dogdayz]

OK, Ok, LOL

938 feet is right (disregard the earth's curvature)


Go eat those chops.....

[really_troubled]

you would need to disregard more than the earth's curvature

obviously the correct answer is 0