Pulley on the dock is 1 m higher than the bow of the boat.

Rope is pulled in at a rate of 1 m/s.

Diagram of situation at any time :

Assume the length of the rope as m at any time .

Rope is pulled in at a rate of 1 m/s.

Thus, , as time increases the length of the rope decreases.

Assume that the boat is m away from the dock at any time .

Apply Pythagorean theorem to the above figure.

.

Differentiate on each side  with respect to .

Determine how fast  the boat is approaching the dock, when it is m away from the dock.

Thus, .

Substitute in .

Substitute , ,  and in  .

Therefore, the boat approaching the dock at a rate of  m/s  when it is m away from the dock.

The boat approaching the dock at a rate of  m/s  when it is m away from the dock.