If a track is 1000m, and you push one end 1m towards the other, how high does the middle rise from the ground?

Question

Assuming the arc created is a circular arc.

I never could figure this one out - I must've had a mental block.

Answer 1

I started to do this, but got lazy. Dr. math explains it well!

Answer 2

We know that the center is 500m from both ends and then ends are 1 m closer making the distance between the ends 999m. If we imagine a right triangle with a base of 499.5 (one half of 999) and a hypotenuse of 500m and reverse the Pythagorean theorem
C^2 - A^2 = B^2 you will get the height

500^2 - 499.5^2 = sqr(499.75) = about 22.4m

Answer 3

0.5m.