Results 1 to 3 of 3

Math Help - Elementary Calculus: Related Rates with Angle Problem

  1. #1
    Newbie
    Joined
    Jan 2011
    Posts
    14

    Elementary Calculus: Related Rates with Angle Problem

    A rocket is launched vertically upward from a point 2 miles west of an observer on the ground. What is the speed of the rocket when the angle of elevation (from the horizontal) of the observer's line of sight to the rocket is 50 degrees and is increasing at 5 degrees per second?

    This is what I have done:

    tan(x) = y/2

    sec^2(x) * dx/dt = (1/2) * dy/dt

    dy/dt = 2sec^2(50) * 5

    dy/dt = 24.2 miles/second

    The actual answer is 0.42 miles/second.

    Any help is much appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7
    Quote Originally Posted by evankiefl View Post
    A rocket is launched vertically upward from a point 2 miles west of an observer on the ground. What is the speed of the rocket when the angle of elevation (from the horizontal) of the observer's line of sight to the rocket is 50 degrees and is increasing at 5 degrees per second?

    This is what I have done:

    tan(x) = y/2

    sec^2(x) * dx/dt = (1/2) * dy/dt

    dy/dt = 2sec^2(50) * 5

    dy/dt = 24.2 miles/second

    The actual answer is 0.42 miles/second.

    Any help is much appreciated.
    You need to convert the angles to radians.

    \displaystyle \frac{dy}{dt}=2sec^2(\frac{50\pi}{180})\times\frac  {5\pi}{180}=0.4224
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2011
    Posts
    14
    Thank you. Why is that so?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Related rates, finding an angle.
    Posted in the Calculus Forum
    Replies: 5
    Last Post: March 28th 2011, 03:17 PM
  2. Related Rates - Calculus Problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: June 1st 2010, 02:43 PM
  3. Help with related rates problem (calculus I)
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 3rd 2009, 04:25 PM
  4. Replies: 1
    Last Post: October 8th 2008, 07:09 PM
  5. [SOLVED] Related rates problem for calculus
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 21st 2008, 07:40 PM

Search Tags


/mathhelpforum @mathhelpforum