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?
=..........m/s
1
Expert's answer
2012-10-29T11:40:50-0400
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].
Therefore,
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.
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