In physics class, the teacher shows us an interesting physics experiment. He hangs an iron chain on a fixed point on the wall. (Look at the right picture for more details). If the lengths of the iron chains on the left side and right side are different, the gravity forces the iron chain to drop to the floor and hits the sensor. Then the computer shows the F-t functional image on the screen. The teacher wants to teach you momentum and its conservation.
But you are not interested in this at all. The thing you want to know is how long it takes for the iron chain to drop to the floor.
You can assume that the iron chain is well-mixed, and you can ignore the friction between the iron chain and the fixed point on the wall. The friction between the chain and the air needn’t be taken into account either. The fixed point is a particle whose radius is 0. And the acceleration of gravity, or so-called g, is 9.80665m/s^2 in this problem.
Example:
1.Input: a=0 ,b=10,h=20
Output: t=1.428s
2.Input: a=1,b=3,h=4
Output: t=0.595s
============Cut-Off Rule===========
I've tried the approximation algorithm.But I couldn't pass through the judge.[I've passed the Examples before.]
And I communicated with CPY about using Calculus to solve this problem,but we couldn't solve the equation.
Who can help me....
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