Question

(1 point) A boat is pulled into a dock by means of a rope attached to a pulley on the dock. The rope is attached to the front of the boat, which is 6 feet below the level of the pulley. If the rope is pulled through the pulley at a rate of 12 ft/min, at what rate will the boat be approaching the dock when 90 ft of rope is out?

The boat will be approaching the dock at ______  ft/min

Previous Problem Problem List Next Problem (1 point) A boat is pulled into a dock by means of a rope attached to a pulley on the dock. The rope is attached to the front of the boat, which is 6 feet below the level of the pulley. If the rope is pulled through the pulley at a rate of 12 ft/min, at what rate will the boat be approaching the dock when 90 ft of rope is out? The boat will be approaching the dock at ft/min Hint: Sketch a diagram of this situation.

Answer 1

Consider the below figure B Pulley os 6 F C Dak Here the ad AB=Y arem A represents the location of bood, B and C represents bulley and dock. any moment Dock to boot distance is pcft and Pulley to bood is gft. Given that BC= 6ft AC From the right angle triangle ABC C, using bythagorean theo (Ac) + CBg4 ABZ + 2?+62 - 42 -0 Differentiate o with respect to t both sides gires 2y d y dd = 2 del mio Given that' dy - Rete at which roke is killed toward pulley Walthin - dy = 12ft/min Plug it St. 2x de pe too = D et 2 da at 124 nu 2 When y=qoft (ie erobe is 9off out then from ® x² = 96²-82 2a 24 Sut in >) &> V20²-6² =2ustu IW u5 ft/min = 124 ao Plug G = 9o and a do Thus, the boat is approaching the dock at us so ft/min. 241 viy کا