Results 1 to 2 of 2

Math Help - Airplanes

  1. #1
    Member
    Joined
    Mar 2008
    Posts
    88

    Exclamation Airplanes

    An airplane is flying at an altitude of 6 miles and passes directly over a radar antenna. When the plane is 10 miles away, the radar detects that the distance s is changing at a rate of 240 miles per hour. What is the speed of the plane?

    The teacher I have loves planes and assigned this problem and many others. I sloved most of them. Thanks for the time
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    by the pythagorean theorem we know that

    6^2+x^2=s^2 and we want to find \frac{dx}{dt} when x=10.

    using the above we know that s=\sqrt{136} when x=10.

    taking the derivative with respect to time

    2x\frac{dx}{dt}=2s\frac{ds}{dt} \iff \frac{dx}{dt}=\frac{s}{x}\frac{ds}{dt}=\frac{\sqrt  {136}}{10}\frac{240 \mbox{ miles}}{\mbox{ hr}}=48\sqrt{34}\frac{miles}{hr}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Airplanes
    Posted in the Trigonometry Forum
    Replies: 10
    Last Post: May 22nd 2010, 09:23 PM
  2. 2 airplanes with different speeds
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 29th 2010, 04:49 PM

Search Tags


/mathhelpforum @mathhelpforum