Advanced Catenary Problems! Really need help!

[eddiesf32197]

1. Two poles are twenty feet apart. One is 10 feet tall, the other is 15 feet tall. A rope 25 feet long hangs between the tops of the two poles. Does it touch the ground? If not, how high above the ground and how far from the shorter pole is the lowest point on the rope?

2. A rod of a given length is pivoted in a vertical plane about its center. A rope of given length hangs from it, attached at both ends. As the rod rotates, the lowest point on the rope traces out a curve. Plot this curve.

So in Class my classmates and I have made three equations for the first problem but are lost to how to solve the problem from there:
10 = acosh(x/a) =b
15 = a(e^(x-20/a) + e^(20-x/a))/2 +b
15 = a(e^(x+c/a) + e^(x-c/a))/2 +b

these questions use the formula for caternarys:
y(x)= acosh(x/a) + b
where cosh(x) = (e^x + e^-x)/2

If someone can help me with this problem I'd be forever indebted to them!! Thank you!

 

[JohnZ]

1. Two poles are twenty feet apart. One is 10 feet tall, the other is 15 feet tall. A rope 25 feet long hangs between the tops of the two poles. Does it touch the ground? If not, how high above the ground and how far from the shorter pole is the lowest point on the rope?

2. A rod of a given length is pivoted in a vertical plane about its center. A rope of given length hangs from it, attached at both ends. As the rod rotates, the lowest point on the rope traces out a curve. Plot this curve.

So in Class my classmates and I have made three equations for the first problem but are lost to how to solve the problem from there:
10 = acosh(x/a) =b
15 = a(e^(x-20/a) + e^(20-x/a))/2 +b
15 = a(e^(x+c/a) + e^(x-c/a))/2 +b

these questions use the formula for caternarys:
y(x)= acosh(x/a) + b
where cosh(x) = (e^x + e^-x)/2

set 10 feet tall pole as the origin.
y(x) = a*cosh(x/a + c1) + c2, where a, c1, c2 are constants
x=0, y(0)=10, => a*cosh(c1) + c2 = 10
x=20, y(20)=15, => a*cosh(20*/a + c1) + c2 = 15
arc length = 25, => Integral from 0 to 20 (1 + sinh(x/a + c1)^2) dx = 25
and this will be sinh(20/a + c1) - sinh(c1) = 25
solve a,c1,c2 use these equations...