Results 1 to 2 of 2

Math Help - Related rates question..here's my work

  1. #1
    Member
    Joined
    Dec 2008
    Posts
    92

    Related rates question..here's my work

    A balloon rises at the rate of 8 feet per second from a point on the ground 60 feet from an observer. Find the rate of change of the angle of elevation when the balloon is 25 feet above the ground.

    My work:

    picture: http://i41.tinypic.com/14j0vuv.jpg

    tan Θ=y/x
    tan Θ=25/60
    Θ = 22.78 degrees

    derivative of tanΘ=y/x:
    sec˛Θ(dΘ/dt) = [ (x)(dy/dt) - (y)(dx/dt) / x˛ ]
    1.176(dΘ/dt) = [ 60(8) - (25)(19.2) / 60˛ ]

    ^^I got the dx/dt number, 19.2 by setting up this proportion:
    60/x = 25/8

    But then I realized that when I solve this:
    60(8) - (25)(19.2), I get 0...what am I doing wrong??


    **EDIT: Sorry, you're right, I meant dx/dt and dy/dt

    Thanks!
    Last edited by janedoe; April 28th 2009 at 08:01 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Mar 2007
    Posts
    1,240

    Talking

    In your picture, it looks like you're using dy/dx for the change in height, but the height y is not changing with respect to the change in the ground-distance x; it is changing with respect to the time t. So it should be "dy/dt = 8".

    Also, since the balloon is rising directly vertically, then the ground-distance x is not changing; dx/dt = 0.

    You have tan(@) = y/x. (I'm using "@" to stand for the angle "theta".) Differentiating with respect to time t, I believe you should get:

    . . . . .sec^2(@) (d@/dt) = [(dy/dt)x - y(dx/dt)] / x^2

    Since the secant is, for right triangles such as this one, equal to "(hypotenuse) over (adjacent)", use the Pythagorean Theorem to find the value of the hypotenuse when y = 25 and x = 60.

    Then plug in the known values for sec(@), dy/dt, dx/dt, x, and y. Solve for d@/dt.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Related Rates - Check my work please
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 6th 2010, 02:42 AM
  2. [SOLVED] Related Rates: Check my work
    Posted in the Calculus Forum
    Replies: 0
    Last Post: September 22nd 2010, 08:13 AM
  3. A question on Related rates.
    Posted in the Calculus Forum
    Replies: 13
    Last Post: July 24th 2010, 12:26 PM
  4. Another Related Rates question
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 7th 2010, 12:34 PM
  5. work check: related rates
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 5th 2009, 11:15 AM

Search Tags


/mathhelpforum @mathhelpforum