A boat is pulled into a dock by a rope attached to the bow ("front") of the boat and passing through a pulley on the dock that is 1m higher than the bow of the boat. If the rope is pulled in at a rate of 1m/s, how fast is the boat approaching the dock when it is 8m from the dock?
We need to find the horizontal component of the end of the rope. The length of a rope is
L = √((8[m])² + (1[m])²) = √65[m].
V = 1[m/s]*cosα = 1[m/s]*8[m]/√65[m] = 8/√65[m/s] ≈ 0.992[m/s],
where α is an angle between the rope and the water.