Engineering Finding arc length of a pipe between two tanks

[knotted_pine]

Homework Statement

I am trying to find the arclength and max height of a pipe between two tanks A and B. The height of A is 0.4km and the height of B is 0.6km.

Relevant Equations

The change in elevation is given by $z^* = a + bx^* + c(x^*)^2$

$z^* = z/0.2km$ and $x^* = x/400 km$

x is the horizontal distance from A and 400 is the horizontal distance from A and B.

The maximum pipe elevation is $x^* = 0.6$

I can't seem to find the arclength between A and B.

I tried using L = integral (0.6 to 0.4) of sqrt (1+ (dz/dx)^2) to no avail.

Would it be roughly similar to 400 km (the length from A to B) since the change in elevation could be considered negligible? Furthermore, how might I go about finding max elevation?

 

[jim mcnamara]

r= radius of the Earth. Arc length requires using r, right? So, what is the radius of the Earth in km?
Since it is an arc, I do not understand why you are concerned about a highest point. 0.6km is the highest point based on what you posted. You also need the angle in radians (or degrees).

So, to help us out, please read the first few paragraphs from the Latex Guide, Blue text Above "Attach files". Your Latex did not render. I cannot tell if you are on the right track.

What does your problem actually ask for?