Frames of Reference: Find the speed and heading of the airplane

[ahira]

Homework Statement

pilot is flying from City A to City B which is 300 km [NW]. If the plane will encounter a constant wind of 80 km/h from the north and the schedule insists that he complete his trip in 0.75 h, what air speed and heading should the plane have?

Relevant Equations

V=d/t
Vg= Vair +Vwing

so far what i have gotten to is that 300/0.75 = 400km/h but I dont know how to draw the diagram for this

 

[Lnewqban]

Welcome, @ahira !
Have you studied addition of vectors?
If so, start by drawing the velocity vectors given by the problem.

Please, see:
https://courses.lumenlearning.com/s...r-addition-and-subtraction-graphical-methods/

https://courses.lumenlearning.com/s...-addition-and-subtraction-analytical-methods/

 

[ahira]

would it be like this?

 

[BvU]

so far what i have gotten to is that 300/0.75 = 400km/h but I dont know how to draw the diagram for this

would it be like this?

'like this' is a good description, but some improvement is in order:

• heading AB is $\pi/4$
• you write $v_g = v_{air} + v_{wing}$, but you draw $v_{wing}= =v_g - v_{air}$. That's fine, but somewhat confusing, especially if you don't label the vectors.

So far, so good; now perform the actual calculation

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[ahira]

'like this' is a good description, but some improvement is in order:

• heading AB is π/4
• you write vg=vair+vwing, but you draw vwing==vg−vair. That's fine, but somewhat confusing, especially if you don't label the vectors.

So far, so good; now perform the actual calculation

I Changed the diagram and realized that North West sits on an angle of 45 degrees so therefore the angle between the Northline and A should be 45 degrees. I'm not that sure but should the angle at B be 45 degrees as well due to alternate angles ?

 

[BvU]

City A to City B which is 300 km [NW]

So vector AB should correspond to the ground speed with a heading of 45 degrees west of north and magnitude 400 km/h. As you wrote$$v_g = v_{air} + v_{wing}$$but now your drawing shows vector AC (a.k.a.$\ \ v_{wing}\ \$) as $v_g + v_{air}$ !!

Lean back a little and use common sense: with a headwind your course should be aiming upwind of A !

And you can also reasonably expect that you need to make more speed than the 400 km/h ('AC should be longer than AB')

$\$

 

[berkeman]

Sorry for the dumb question, but should $v_{wing}$ be $v_{wind}$ in all of the posts above (including the OP's)?

 

[BvU]

somewhat confusing, especially if you don't label the vectors.

I feel dumb for taking $v_{air} =$ 80 km/h from the north (the speed OF the air ), when - most likely -@ahira perhaps meant $v_{air} =$ the speed WRT the air.

So what about

Relevant Equations:
Vg= Vair +Vwing

and the picture in #3 ?

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