- #1
RedBarchetta
- 50
- 1
Homework Statement
A jetliner with an airspeed of 1000 km/h sets out on a 1500-km flight due south. To maintain a southward direction, however, the plane must be pointed 15 degrees west of south. If the flight takes 100 min, what is the wind velocity?
The Attempt at a Solution
This one has been giving me issues. What do you do here? Does 'airspeed' mean that the plane is traveling 1000 km/h with respect to the air? Here is what I've tried:
First of all, I find the components of the jetliner. I take -y to be south and +x to be east.
[tex]\[
\overrightarrow {V_{pa} } = 1000 \cdot \cos (15^ \circ )i + 1000 \cdot \sin (15^ \circ )j
\][/tex]
So there is the velocity vector with respect to the air. Now from this equation, I can multiply by the time 100min or (5/3)h, to get the displacement vector:
[tex]\[
\overrightarrow {R_{net} } = \frac{5}
{3}1000 \cdot \cos (15^ \circ )i + \frac{5}
{3}1000 \cdot \sin (15^ \circ )j
\]
[/tex]
I'm not quite sure what to do after this...How do you find the wind velocity from this?
My book says the answer is:
[tex]\[
(259km/h)i + (65.9km/h)j
\]
[/tex]