1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Trigonometric Problem

  1. May 24, 2005 #1


    User Avatar
    Homework Helper

    Hello, I'm in need of a hint or few pointers on how to calculate the angle C of the picture attached. I've already calculated y.

    I was doing a few problems in this Dynamics book, i bought recently, and the ascention angle (angle C) is beating me :eek:

    "The airplane C is being tracked down by the radar stations A and B. At the instant shown on the picture, the triangle ABC encounters itself in vertical plane and the lectures are Angle A = 30 degrees, Angle B = 22 degrees, Angular Speed A = 0.026 rad/s, Angular Speed B = 0.032 rad/s. Find a) the height y, b) the magnitude of the velocity (the vector V is at point C directed at an ascention angle (angle C) with respect tot he horizontal c) the ascention angle at the instant shown (angle c)"

    ah yes distance d = 1000 m and it's between the stations A and B.

    I hope the diagram is clear enough...

    Attached Files:

    Last edited: May 24, 2005
  2. jcsd
  3. May 24, 2005 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    A few hints:
    1) Having "y", it is easy determine lengths of AC, BC, and form the vector from A to C, and the vector from B to C.
    Let for example the vector from AC have the form [tex]\vec{r}_{AC}=r_{AC}\hat{r}_{AC}[/tex]
    where [tex]r_{AC},\hat{r}_{AC}[/tex] are the length and direction vector, respectively.

    2) Let [tex]\hat{n}_{AC}[/tex] be the unit vector in the plane of the triangle perpendicular to [tex]\hat{r}_{AC}[/tex] and pointing in the direction of increasing angle, and make a similar construction for [tex]\hat{n}_{BC}[/tex]

    3) Decompose your velocity as:

    4) We therefore have, for example the equality:
    where [tex]\omega_{AC}[/tex] is the angular velocity measured at A.

    5) Thus, we have determined [tex]\vec{v}[/tex] and may answer the two remaining questions.
    Remember that [tex]\hat{r}_{AC},\hat{r}_{BC}[/tex] are not orthogonal vectors!
    Last edited: May 24, 2005
  4. May 24, 2005 #3


    User Avatar
    Homework Helper

    Thanks Arildno, i was able to solve it. :biggrin:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook