Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

NickR Group Title

A kite 50ft above the ground moves horizontally at a speed of 8ft/s. At what rate is the angle between the string and the horizontal decreasing when 300ft of string has been let out?

  • one year ago
  • one year ago

  • This Question is Closed
  1. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1351143411523:dw|

    • one year ago
  2. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    tan(theta) = 50/x differentiate both sides with respect to time find x when sqrt(x^2+50^2) =300 (*spoiler*) find theta when x= sqrt(300^2 -50^2) plug x, theta and dx/dt into the result of the differentiation to find d(theta)/dt

    • one year ago
  3. NickR Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    can you explain the diferrentiatie both sides with respect to time part?

    • one year ago
  4. NickR Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @Algebraic!

    • one year ago
  5. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I guess, it's just implicit differentiation really...or the chain rule... or whatever you are comfortable thinking of it as... d/dt ( tan ( f(t) ) =

    • one year ago
  6. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    derivative of the 'outside' is...?

    • one year ago
  7. NickR Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    sec^2

    • one year ago
  8. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    :)

    • one year ago
  9. NickR Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    so it's x = 50/sec^2(theta)?

    • one year ago
  10. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yep, so sec^2 (f(t) ) * f '(t)

    • one year ago
  11. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    f(t) is theta yeah, I wrote it that way because theta depends on time and I wanted you to see the chain rule

    • one year ago
  12. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    so LHS is sec^2(theta) * d(theta) /dt RHS still needs to be differentiated...

    • one year ago
  13. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    d/dt ( 1/(g(t)) ) =...?

    • one year ago
  14. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    -1/ ..........

    • one year ago
  15. NickR Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    what is g(t) in this case?

    • one year ago
  16. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    well, just because I used f(t) for theta... now we're talking about x, which is a different function of time...

    • one year ago
  17. NickR Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    ah okay

    • one year ago
  18. NickR Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    -1/x^2*dx/dt

    • one year ago
  19. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    great:)

    • one year ago
  20. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    so:\[\frac{ d \theta }{dt } = \frac{ -1 }{x^2 \sec^2\theta }\frac{ d x}{ dt }\]

    • one year ago
  21. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    dx/dt is given.. x and theta are easy to find...

    • one year ago
  22. NickR Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    dx/dt = 8

    • one year ago
  23. NickR Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    d(theta)/dt = -8/x^2*sec(theta)

    • one year ago
  24. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    x= sqrt(300^2 -50^2) theta = arctan (50/x)

    • one year ago
  25. NickR Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    wouldn't x = sqrt(300^2 + 50^2)?

    • one year ago
  26. NickR Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    x = 304.138

    • one year ago
  27. NickR Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    theta = .1629 rads

    • one year ago
  28. NickR Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @Algebraic!

    • one year ago
  29. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    so x is longer than the hypotenuse?

    • one year ago
  30. NickR Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    x = 295.803

    • one year ago
  31. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    k:)

    • one year ago
  32. NickR Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    so d(theta)/dt = -8/((295.803)^2*(sec^2(.16744 rads)) which is incorrect.

    • one year ago
  33. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    -8.87E-5?

    • one year ago
  34. NickR Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    well you said d(theta)/dt = -1/(x^2*sec^2(theta)) * dx/dt

    • one year ago
  35. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

    • one year ago
  36. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    you didn't get -8.87E-5?

    • one year ago
  37. NickR Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yes I did

    • one year ago
  38. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    and it says it's wrong...

    • one year ago
  39. NickR Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    yep

    • one year ago
  40. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    dunno let me look it all over. I don't see any glaring mistakes...

    • one year ago
  41. NickR Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    alright

    • one year ago
  42. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    -8.89E-5 rad.s/sec .. best I can do... let's see who else is on, might be able to see if I made a mistake...

    • one year ago
  43. RolyPoly Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    May I have the answer to the question?

    • one year ago
  44. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    go for it.

    • one year ago
  45. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    @eSpeX

    • one year ago
  46. NickR Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @RolyPoly id like the answer too!

    • one year ago
  47. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    @callisto is checking it over...

    • one year ago
  48. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    ty @Callisto

    • one year ago
  49. Callisto Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I... am no good at maths... \[tan \theta = \frac{50}{x}\] Differentiate both sides with respect to x. Probably you won't get: \[\frac{ d \theta }{dt } = \frac{ -1 }{x^2 \sec^2\theta }\frac{ d x}{ dt }\]

    • one year ago
  50. Callisto Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    My bad, I meant with respect to t

    • one year ago
  51. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    you're saying the differentiation is wrong?

    • one year ago
  52. Callisto Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[tan \theta = \frac{50}{x}\] Diff. both sides w.r.t. t \[sec^2\theta \frac{d\theta}{dt} = \frac{-50}{x^2} \frac{dx}{dt}\]\[\frac{d\theta}{dt} = \frac{-50}{x^2sec^2\theta } \frac{dx}{dt}\]

    • one year ago
  53. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    arg

    • one year ago
  54. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    forgot the 50 rfl

    • one year ago
  55. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    you so smart cally

    • one year ago
  56. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    :)

    • one year ago
  57. NickR Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    -50*-8/((295.803^2)*sec^2(.16744)) = correct answer

    • one year ago
  58. NickR Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    thank you @Callisto and @Algebraic!

    • one year ago
  59. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yes thanks @Callisto !

    • one year ago
  60. Callisto Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    \[sec^2\theta=\frac{x^2+50}{x^2}\]You can cancel the x^2 since \[\frac{d\theta}{dt} = \frac{-50}{x^2sec^2\theta } \frac{dx}{dt}=\frac{-50}{x^2(\frac{x^2+50}{x^2}) } \frac{dx}{dt}\]\[=\frac{-50}{(x^2+50) } \frac{dx}{dt}\]And x^2 is easy to find

    • one year ago
  61. NickR Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    only took me 4hrs but i got my question worth 1pt right now to get some sleep

    • one year ago
  62. Algebraic! Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    heh

    • one year ago
  63. NickR Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    you guys have a good night thanks again

    • one year ago
  64. Callisto Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Good night!!~

    • one year ago
  65. robtobey Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    A revised Mathematica solution, posted on 25 October 2012, 22:15 California time, is attached.

    • one year ago
    1 Attachment
    • Attachments:

See more questions >>>

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.