1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Related rates help

  1. Nov 17, 2011 #1

    nyr

    User Avatar

    Theres two parts to the question. Each part also has two parts to it. Im pretty sure my work i did so far is correct( double check please) but im not sure about the bolded parts

    A boat is pulled into a dock by means of a winch 12 feet above the deck of the boat.?


    a) The winch pulls in rope at a rate of 4 feet per second. Determine the speed of the boat when there is 13 feet of rope out. What happens to the speed of the boat as it gets closer to the dock?


    b) Suppose the boat is moving at a constant rate of 4 feet per second. Determine the speed at which the winch pulls in rope when there is a total of 13 feet of rope out. What happens to the speed at which the winch pulls in rope as the boat gets closer to the dock?
    ______________________________________________________


    a) The boat is 5 ft from the dock. (5-12-13 rt triangle)
    Let a = distance from dock, b = height of dock, and c = length of rope.

    a^2 + b^2 = c^2
    2a da/dt + 2b db/dt = 2c dc/dt
    a da/dt + b db/ddt = c dc/dt
    5 da/dt + 12(0) = 13 • -4
    5 da/dt = -52
    da/dt = -10.4
    The boat is going -10.4 ft/sec.


    b) a da/dt + b db/dt = c dc/dt
    5 • 4 + 12(0) = 13 dc/dt
    20 = 13 dc/dt
    1.5384... = dc/dt
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Related rates help
  1. More Related Rates (Replies: 0)

Loading...