Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

eva12

  • 2 years ago

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 7 feet below the level of the pulley. If the rope is pulled through the pulley at a rate of 10 ft/min, at what rate will the boat be approaching the dock when 100 ft of rope is out?

  • This Question is Closed
  1. baldymcgee6
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1350689236706:dw|

  2. eva12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    how do you get the answer or solve it?

  3. baldymcgee6
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You must find a way to relate rate of the pully rope to the rate of the boat using the right angle triangle

  4. eva12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i do not understand this problem or how to approach it to solve it

  5. eva12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    can someone help me

  6. baldymcgee6
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1350690450622:dw|

  7. baldymcgee6
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you can express the triangle as 7^2 + x^2 =r^2

  8. eva12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    then what will x be and would r will stand for rate rigth

  9. baldymcgee6
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\frac{ dr }{ dt } = -10ft/\min\]\[\frac{ dx }{ dt }|_{r=100}\]

  10. baldymcgee6
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I'm just calling r the length of ROPE

  11. eva12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so the equation 7^2+x^2=r^2 will be dr/dt=2x+2r

  12. baldymcgee6
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    when we differentiate 7^2 + x^2 =r^2, we will get: 49 + 2x* dx/dt = 2r* dr/dt

  13. eva12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    then i pug in 100 for r and 10 for x in the equation

  14. baldymcgee6
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no, dr/dt = -10 ft/min.. we don't know what x is

  15. eva12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    49 +2x=2(100)= will = x is 75.5

  16. baldymcgee6
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no, we don't solve for x as x is always changing. that is essentially what the question is asking.

  17. eva12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so then how do i approach then

  18. baldymcgee6
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    okay... so here's what we do, we have to equations that will help us solve this problem, namely: 7^2 + x^2 =r^2 49 + 2x* dx/dt = 2r* dr/dt are you with me so far?

  19. eva12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    do i solve for 1 equation then the 2 one

  20. baldymcgee6
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    First lets deal with this equation: 49 + 2x* dx/dt = 2r* dr/dt what are we looking for, well the question asks, "at what rate will the boat be approaching the dock?" The rate at which the boat is approaching the dock is represented by dx/dt (the rate of change of x), so we need to re arrange this equation for dx/dt

  21. eva12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    dx/dt=2r*dr/dt-49/2x

  22. baldymcgee6
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    good.. what do we know, we know what dr/dt is, and we know what that r=100 at the point of interest. but we don't know what x is at this given instance, so what we need to do is express x in terms of r in the other other equation: 7^2 + x^2 =r^2 x = sqrt(r^2-49) now substitute that into our change of rates equation, and we know that r =100, and dr/dt= -10: dx/dt = (2(100)*(-10)-49)/2(sqrt(100^2-49) = your answer

  23. eva12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    -102198.6893

  24. baldymcgee6
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no, it shouldn't be that big

  25. baldymcgee6
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you must have typed it in wrong in your calculator

  26. eva12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    -10.27

  27. eva12
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks

  28. baldymcgee6
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you're very welcome

  29. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.