Question

Two ropes are attached to the ceiling at points root3 meters apart. The rope on the left is 1 meter long and has a pulley attached at its end. The rope on the right is 3 meters long; it passes through the pulley and has a weight tied to its end. When the weight is released, the ropes and pulley arrange themselves so that the distance from the weight to the ceiling is maximized.

a) Show that the maximum distance occurs when the weight is exactly halfway between the points where the ropes are attached to the ceiling. [Hint: Write the vertical