Kinematics Question -- Plane heading to take into a headwind

In summary: With the North wind, however, airspeed and ground speed will not be the same. So how do you have to rewrite the equation to correct for the North wind?
  • #1
Hannahj1
18
2

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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  • #2
You didn't describe your triangle. Note that "hypotenuse" and "pythagorean theorem" only apply to right triangles.
 
  • #3
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?
 
  • #4
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
 
  • #5
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 - ?
 
  • #6
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.
 
  • #7
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?
 
  • #8
i figured it out thank you!
 

Related to Kinematics Question -- Plane heading to take into a headwind

1. How does headwind affect the speed of a plane?

Headwind is a wind that blows directly against the direction of motion of a plane. This means that the plane will experience a resistance force, which will decrease its speed.

2. How can we calculate the change in speed due to headwind?

The change in speed can be calculated using the formula: change in speed = headwind speed - plane's airspeed. This will give us the difference between the actual speed of the plane and the speed it would have if there was no headwind.

3. Does headwind affect the plane's direction of motion?

Yes, headwind can also affect the plane's direction of motion. The resistance force from headwind can push the plane off course, causing it to drift in a different direction.

4. How can pilots compensate for headwind during a flight?

Pilots can compensate for headwind by adjusting the plane's airspeed and direction. They can also use navigation tools, such as a compass and GPS, to ensure the plane stays on course.

5. Can headwind affect the fuel efficiency of a flight?

Yes, headwind can affect the fuel efficiency of a flight. The resistance force from headwind requires the plane to use more fuel to maintain its speed, which can result in higher fuel consumption and decreased overall efficiency.

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