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Trigonometric Problem

  1. May 24, 2005 #1

    Pyrrhus

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    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...
     

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

    arildno

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    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:
    [tex]\vec{v}=v_{AC}\hat{r}_{AC}+v_{BC}\hat{r}_{BC}[/tex]

    4) We therefore have, for example the equality:
    [tex]\vec{v}\cdot\hat{n}_{AC}=r_{AC}\omega_{AC}\to{v}_{BC}\hat{r}_{BC}\cdot\hat{n}_{AC}}=r_{AC}\omega_{AC}\to{v}_{BC}=\frac{r_{AC}\omega_{AC}}{\hat{r}_{BC}\cdot\hat{n}_{AC}}[/tex]
    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

    Pyrrhus

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    Thanks Arildno, i was able to solve it. :biggrin:
     
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