how do I solve this?

Question

A rope, attached to a weight, goes up through a pulley at the ceiling and back down to a worker. The worker holds the rope at the same height as the connection point between the rope and weight. The distance from the connection point to the ceiling is 45 ft. Suppose the worker stands directly next to the weight (i.e., a total rope length of 90 ft) and begins to walk away at a constant rate of 2 ft/s. How fast is the weight rising when the worker has walked:

Answer 1

If you just want to know how to solve this, since the rope is going through a pulley, the rate that the weight is rising will be the same as the rate that the length of the rope from the pulley to the worker is increasing.

Just write an expression for the right triangle in the form

s²=45²+x²

Where s = the length of the rope from the worker to the pulley.

Take the derivative and solve for ds/dt, plugging in the values you know. x will be the distance from the worker to the original position of the weight.