A boat is pulled toward a dock by means of a rope wound on a drum that is located 4 ft above the bow of the boat

rope-wound-drum

#1

A boat is pulled toward a dock by means of a rope wound on a drum that is located 4 ft above the bow of the boat. If the rope is being pulled in at the rate of 5 ft/sec, how fast is the boat approaching the dock when it is 27 ft from the dock? (Round your answer to one decimal place.

Answer:

this requires basic trig knowledge. So you can set up a triangle with side lengths of horizontal 27 ft vertical 4 ft (orientation doesnt matter since the boat is always moving towards the dock which is a positive velocity) if you take arctan(y/x) you’ll get theta. use theta to find the horizontal component of velocity. I did this equation on paper and got theta was 8.426969 which is almost negligible. Rounded to one decimal place you’ll get 4.9 ft/s for x-comp of velocity. Hope this helps, trig is fun!