0

A plane heads at an angle of 30 degrees west of north at a speed of 250m/s. Calculate the westward and northward components of the planes velocity

Nayeli Montemayor
  • 1
  • 4
    Hi, would you like to edit your post to include what you have tried? It is likely to get more positive responses that way. – Siong Thye Goh Aug 22 '18 at 04:25
  • 2
    Please edit your question to provide some additional context. For example, where does this problem come from? Why are you interested in it? Is it for a class? If so, what class? What tools (theorems, definitions, etc) do you expect to use to solve this problem? Have you made any attempt at a solution? If so, what, and where did you get stuck? etc... – Xander Henderson Aug 22 '18 at 04:26

1 Answers1

1

enter image description here

Velocity of the plane is represented with vector $\vec{AC}$ and the magnitude of that vector is $AC=250\frac ms$. On the other side $\vec{AC}=\vec{AB}+\vec{BC}$, with $\vec{AB}$ representing the northward and $\vec{BC}$ representing the westward component of velocity.

You can easily calculate magnitudes of these two components if you notice that $\triangle ABC$ is actually a half of the equilateral triangle $\triangle ADC$:

$$BC=\frac12 AC=\frac12 \cdot 250 \frac ms = 125\frac ms$$

$$AB=\frac{\sqrt{3}}{2} AC=\frac{\sqrt{3}}{2} \cdot 250 \frac ms = 125\sqrt3\frac ms\approx 216.5\frac ms$$

Saša
  • 15,906