Question

A cable hangs between two poles of equal height and 40 feet apart.
At a point on the ground directly under the cable and
x feet from the point on the ground halfway between the poles
the height of the cable in feet is

h(x)=10+(0.4)(x^1.5).
The cable weighs 18.2 pounds per linear foot.
Find the weight of the cable.

Answer 1

You want the arc length of the cable. Just figure the length from the center and double it.

dh/dx = 0.6√x
so, the arc length from the center to the pole is just

∫[0,20] √(1+.36x) dx
= 50/27 (1+.36x)^(3/2) [0,20]
= 41.63

So, the cable weighs 18.2*2*41.63 = 1515.3 lbs

Answer 2

thank u