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.
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!