Results 1 to 2 of 2

Math Help - related rates!

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    42

    Exclamation related rates!

    A highway patrol plane flies 1 mile above a straight section of rural interstate highway at a steady ground speed of 120 miles per hour. The pilot sees an oncoming car and, with radar, determines that the line-of-sight distance from the plane to the car is 1.5 miles and that this distance is decreasing at a rate of 136 miles per hour. Should the driver of the car be given a ticket for speeding?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    Quote Originally Posted by cottekr View Post
    A highway patrol plane flies 1 mile above a straight section of rural interstate highway at a steady ground speed of 120 miles per hour. The pilot sees an oncoming car and, with radar, determines that the line-of-sight distance from the plane to the car is 1.5 miles and that this distance is decreasing at a rate of 136 miles per hour
    .

    Use Pythagoras and your given info to set up the problem and find the rate

    at which the driver is going.

    The hypoteneuse of the triangle formed is length 3/2 and dD/dt=-136.

    dy/dt=0 because the chopper is at a constant height of y=1.

    Since y=1 and D=3/2, then use Pythagoras to find the horizontal distance

    the car is from the chopper.

    The chopper is flying at 120 if we label that side of the triangle x and let

    dx/dt=120. The trick is noting that the chopper and the car are

    approaching one another. The chopper at dx/dt=120 and the car at, say, dz/dt=?

    That is what must be found.


    Should the driver of the car be given a ticket for speeding?
    That depends. What's the speed limit and how hard-nosed is the cop?.
    Attached Thumbnails Attached Thumbnails related rates!-car-cop.gif  
    Last edited by galactus; November 24th 2008 at 09:21 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Related Rates
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 26th 2009, 08:54 PM
  2. Rates and Related Rates!!
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 2nd 2008, 10:53 AM
  3. Another Related Rates
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 13th 2008, 06:32 AM
  4. Related Rates
    Posted in the Calculus Forum
    Replies: 6
    Last Post: March 12th 2008, 05:49 PM
  5. rates and related rates
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 29th 2007, 09:51 PM

Search Tags


/mathhelpforum @mathhelpforum