# Thread: relative velocity and plane

1. ## Re: relative velocity and plane

ok i am getting the right answer finally.
i can only get the right answer using the diagram i originally posted up . however it does not make sense in a different way cause they give you the direction of the plane relative to the air in the question.

i think there is a mistake in the question and it should say what is the direction of the plane relative to the wind and not relative to the air

2. ## Re: relative velocity and plane

i am now trying to figure it out after 16:30.
i am not getting the right answer of 34.8 west of south.
any idea how to get this anyone?

3. ## Re: relative velocity and plane

let me work on it ...

4. ## Re: relative velocity and plane

i can posted worked examples from the chapter if you need them. or anything else let me know

5. ## Re: relative velocity and plane

Thanks, but I used to do this for a living ...

6. ## Re: relative velocity and plane

airplane flies relative to the air mass ... air mass moves (we call that wind) ... airplane moves relative to the Earth (the ground or sea, whatever)

so, the following vector equation is always true ...

air vector + wind vector = ground vector

1500 -1630 ... see 1st diagram

law of sines yields the equation $\dfrac{\sin{\theta}}{100}=\dfrac{\sin(45)}{200} \implies \theta \approx 20.7^\circ$

air vector direction is 65.7 deg S of W or 24.3 deg W of S

groundspeed using law of sines is $|G|=257.8 \, km/hr$

from 1500-1630, distance traveled is 386.7 km

1630 - on ... see 2nd diagram

$\dfrac{\sin{\phi}}{50} = \dfrac{\sin(135)}{200} \implies \phi \approx 10.2^\circ$

air vector direction is 55.2 deg S of W or 34.8 deg W of S

new groundspeed using law of sines is $|G|=161.5 \, km/hr$

airport Q is 600 km total ... 213.3 km left to go on this leg $\implies t = \dfrac{213.3}{161.5} \approx 1.3 \, hrs = 1 \, hr + 18 \, min$

... should get to Q at about 1748-ish.

7. ## Re: relative velocity and plane

thanks a lot. this clears up a lot. thanks

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