Kinematics Question -- Plane heading to take into a headwind

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Homework Statement



A 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?

Homework Equations


v=d/t

The Attempt at a Solution


I found the initial v -> 300/0.75 = 400 km/h. I then used that as the hypothenuse of the triangle and did pythagorean theorem to find the third side. The answer is 460 km/h [N38°W]
 

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Hannahj1 said:

Homework Statement



A 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?

Homework Equations


v=d/t

The Attempt at a Solution


I found the initial v -> 300/0.75 = 400 km/h. I then used that as the hypothenuse of the triangle and did pythagorean theorem to find the third side. The answer is 460 km/h [N38°W]
Hi Hannahj1. Is there a question you wish to ask regarding this?
 
NascentOxygen said:
Hi Hannahj1. Is there a question you wish to ask regarding this?

yeah oops how would i solve the question because my method was wrong
 
Hannahj1 said:
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?

In which direction does the wind blow ; i.e. , North to - ?
 
Hannahj1 said:
yeah oops how would i solve the question because my method was wrong
The first step is to draw a clear, large diagram and mark on it all the information you are given. You will need to make a few attempts at drawing the diagram, it's not always easy to get the triangle right on your first try.

Attach your sketch here.
 
Without the wind you'd have T√(vx2 + vy2) = 300, right? (T = 3/4 hr.) vx and vy are ground speed of course. Airspeed and ground speed would be the same.

With the North wind, however, airspeed and ground speed will not be the same.

So how do you have to rewrite the above equation in terms of airspeed components to correct for the 80 km/h North wind?
 
i figured it out thank you!