# Thread: relative velocity and plane

1. ## relative velocity and plane

an aircraft flies horizontally at a speed 200 km hr^-1 relative to the air. its position at 15:00 is p. a wind with speed 100 km hr^-1 blows from the east from 15:00 to 16:30 . the wind then changes to a speed of 50 km hr^-1 from the south. the aircraft adjusts its heading so it maintains a south westerly course all the time.

find the magnitude and direction of the of the aircrafts velocity relative to the air both before and after 16:30. also if airport q is 600 km south west of p find the time when the aircraft rrives at q.

i cant really visualize the wind and the direction in the aircraft should fly at for both the times. i am trying to label Va=aircraft vector , Vw=wind vector and Vaw =vector of the aircraft relative to the wind

2. ## Re: relative velocity and plane

Vaw has a direction of SW. Vw has a direction of E (between 15:00 and 16:30). Va=Vaw-Vw

3. ## Re: relative velocity and plane

Then what direction is Va ?. I would I thought Va has a direction SW as it says the aircraft heads in a south west direction all the time.

4. ## Re: relative velocity and plane

The final destination is SW. So, after wind pushes the airplane, it needs to be traveling SW. Whatever direction it heads is Va. Its final direction is Vaw

5. ## Re: relative velocity and plane

i would of thought it was like this but i think its wrong?.

6. ## Re: relative velocity and plane

it it not Vaw is the direction it intends to head and Va is the is the actual direction it travels.

im quite confused.

in my diagram the plane knows its getting a little push in the minus i direction so it knows it doesnt have to travel as fast in the minus i direction so it reduces its speed om the minus i direction so you get a steeper Vaw .

7. ## Re: relative velocity and plane

i am reading back on past worked examples and usually Va represents the straight journey i.e from P to the lighthouse.

8. ## Re: relative velocity and plane

Originally Posted by markosheehan
it it not Vaw is the direction it intends to head and Va is the is the actual direction it travels.

im quite confused.

in my diagram the plane knows its getting a little push in the minus i direction so it knows it doesnt have to travel as fast in the minus i direction so it reduces its speed om the minus i direction so you get a steeper Vaw .
I have told you the answer already. You do not seem to want to hear it, but in your drawing, where you wrote Vaw, that should be Va. Where you wrote Va, that should be Vaw.

9. ## Re: relative velocity and plane

anyway, i can not understand the first part of the question when it asks for the magnitude and direction of the of the aircrafts velocity relative to the air both before and after 16:30. for before is it not given to you that its 200 km hr^-1 in a direction SW.

at the back of the book the answer says 200 km hr^-1 west of south. i have no idea where this comes from

10. ## Re: relative velocity and plane

what about this though "i am reading back on past worked examples and usually Va represents the straight journey i.e from P to the lighthouse."

11. ## Re: relative velocity and plane

ok sorry i think i get it. so Vaw stands for after the wind has blown the direction it is heading in. this kind of contradicts my book.

12. ## Re: relative velocity and plane

Originally Posted by markosheehan
ok sorry i think i get it. so Vaw stands for after the wind has blown the direction it is heading in. this kind of contradicts my book.
Then keep Vaw where you had it. |Vaw| = 200.

13. ## Re: relative velocity and plane

When I do what you said I get the direction to be 65.7 degrees west of south. The book says the answer is 24.3 degrees west of south.

I am using the cosine and sine rule

14. ## Re: relative velocity and plane

Then perhaps I'm misreading the question. Its it saying that the plane's total speed (after being pushed by the wind) is 200? Because that would correspond to your drawing exactly. My recommendation is the reading that the plane's speed before being pushed by the wind (relative to the wind) is 200.

15. ## Re: relative velocity and plane

is it not that the plane is capable of flying at 200 not after being pushed it flies at 200.

i going to draw out every possible way and solve all of them until i get an answer that matches the back of the book. i will then know which way is right. ill post back very soon

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