Simple bucket lifting problem statics/physics

[frank1234]

Homework Statement

A worker is trying to lift a 100lb bucket. Assume that the bucket is in static equilibrium as it is raised from 2ft to 18ft. Find the tension in the rope as a function of y.

Homework Equations

The Attempt at a Solution

I solved for angle, a, which cam out to be: arctan(4/(20-y))

Then I solved for the x and y components of the tension vector using: T_x=50lb(a+90) and T_y=50lb(a+90)
I divided the weight by 2 because there are 2 ropes

Then I solved for tension with: sqrt(T_x^2+T_y^2)

The problem I am seeing is that the tension is constant at 30lb no matter the angle, a. I do not think that this should be the case. Could somebody point out where I went wrong? Thank you!

 

[CWatters]

T_y=50lb(a+90) is wrong. Have another think.