A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing


  • 4 years ago

The magnitude of a velocity vector is called speed. Suppose that a wind is blowing from the direction N45°W at a speed of 50 km/h. (This means that the direction from which the wind blows is 45° west of the northerly direction.) A pilot is steering a plane in the direction N60°E at an airspeed (speed in still air) of 200 km/h. The true course, or track, of the plane is the direction of the resultant of the velocity vectors of the plane and the wind. The ground speed of the plane is the magnitude of the resultant. Find the true course and the ground speed of the plane.

  • This Question is Closed
  1. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    This is possibly one of the easiest cal problems ever...

  2. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Hi Krystal, this is not the easiest calculus question ever. To solve this problem, you must figure out (in vector form) both the wind vector (let's call it \[\vec{w}\]and the plane vector \[\vec{P}.\] Then true course of the plane will then be the sum of these two vectors: \[\vec{w}+\vec{P},\] with the ground speed being the norm of this resultant vector: \[\text{ground speed} = || \vec{w} +\vec{P}|| \] In the picture attached to this message, I have drawn (thanks to geogebra) a planar representation of your situation. Use this key to understand: \[\vec{w}=\overline{AB}, \ \ \ \vec{P}=\overline{AC}\] the smaller circle is of radius 50 (same as wind speed) and the larger circle is of radius 200 (same as plane speed). To get the coordinates of these two vectors, it's easiest to use polar coordinates. We let due East be 0 degrees, so since the wind vector is on the circle of radius 50, we have:\[\vec{w}=\langle 50\cos(135),50 \sin(135)\rangle=\langle-25\sqrt{2}\,,\ 25\sqrt{2} \rangle.\] Since the plane vector is on the circle of radius 200, we have \[\vec{P}= \langle 200\cos(60),200\sin(60)\rangle=\langle100\,,\100\sqrt{3} \rangle. \] Hence, the resultant force (or the true course of the plane) is \[\vec{w}+\vec{P}=\langle100-25\sqrt{2}\ ,\ 100\sqrt{3}+25\sqrt{2} \rangle\] FInally, to find the ground speed you take the norm of this vector:\[||\vec{w}+\vec{P}||=\sqrt{(100-25\sqrt{2})^2 +(100\sqrt{3}+25\sqrt{2})^2}\approx218.349218.\] The vector coordinates of \[\vec{w}+\vec{P}\] tell you the true course, and the norm of that vector tells you the ground speed.

    1 Attachment
  3. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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...


  • 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.