# Solving Vector Problems: Finding an Airplane's Ground Speed and Direction

• O0ZeRo00
In summary, the airplane is travelling at 261.8 km/h relative to the ground, due north, and there is a wind blowing at 55 km/h to the northeast.
O0ZeRo00
An airplane flies due north at 220 km/h relative to the air. There is a wind blowing at 55 km/h to the northeast relative to the ground. What are the plane's speed and direction relative to the ground?

I started by using the law of Cosines.
a^2 = b^2 + c^2 - 2bccos(a)
That's the only thing I could think to try.

Have you tried drawing a vector diagram?

first, make a diagram of the thing on the cartesian plane...assume the wind is blowing 45 degrees east of north...draw in the magnitudes(the speed). figure out the other leg when you drop it down to the x axis...if you know what i am talking about. see where that takes you

ideasrule said:
Have you tried drawing a vector diagram?
Yes, I have. Which is where I got the idea for the Law of Cosines.

Oh, ok. You can use the law of cosines to figure out the magnitude of the resultant vector, but it's easier to add the x and y components of the two velocity vectors to get the x and y components of the resultant velocity vector.

Okay. I've solved it. It was 271.79 Km/h at 8.54 degrees east of north.
:]

if you make the diagram...and add the 2 velocity vectors...you end up with...

220sin90 y(hat) + 220cos90 x(hat)
55sin45 y(hat) + 55cos45 x(hat)

add them up using the x and y components as variables...getting a total of...
258.9 y(hat) + 38.9 x(hat)

Your resultant vector is absolute value of R = square root of x^2 + y^2
this will get you your magnitude of 261.8. so this is the final speed.

THen to get the angle it is going...do arc tan of y/x...so 38.9/258.9
you get it will be heading 8.5 degrees east of north.

for some reason i don't like that answer all to much...maybe someone can check me on it but that is how you do it

Last edited:
Well, I know it's correct because I submit my answers onto a website that checks to see if it's right or not.

I sent in mine before i saw your answers...so. did you check your velocity? i double checked mine and it seems to come to the same every time...yours is right says your website?

Hmm... That's odd because mine comes out right too.

Ahh! Nevermind. Typo. Mine actually was 261.79. My bad. Ha.

oh well...its been awhile since i got my lesson on vector addition so i would take yours hehe. feel free to help me with my current vector problem locatedo n the front page of the forums haha

## 1. How do you find an airplane's ground speed and direction?

To find an airplane's ground speed and direction, you need to use vector addition. This involves breaking the airplane's velocity into its components (horizontal and vertical), and then adding them to the wind velocity. The resulting vector will give you the airplane's ground speed and direction.

## 2. What is the importance of solving vector problems in aviation?

Solving vector problems is crucial in aviation as it allows pilots and air traffic controllers to accurately determine an airplane's ground speed and direction, which are important factors in flight planning, navigation, and communication with other aircraft.

## 3. What are the key principles in solving vector problems?

The key principles in solving vector problems are understanding vector components, using vector addition or subtraction, and applying trigonometric functions to determine magnitude and direction.

## 4. How does wind affect an airplane's ground speed and direction?

Wind can have a significant impact on an airplane's ground speed and direction. A headwind will decrease the ground speed and change the direction, while a tailwind will increase the ground speed and change the direction. Crosswinds can also affect the direction of an airplane's travel.

## 5. What are some real-life applications of solving vector problems in aviation?

Solving vector problems is used in aviation for various purposes, such as determining an airplane's true airspeed, calculating the drift angle, and determining the required heading for a flight. It is also essential in aircraft navigation, instrument flying, and flight planning.

• Introductory Physics Homework Help
Replies
10
Views
1K
• Introductory Physics Homework Help
Replies
5
Views
4K
• Introductory Physics Homework Help
Replies
72
Views
7K
• Introductory Physics Homework Help
Replies
4
Views
2K
• Introductory Physics Homework Help
Replies
3
Views
1K
• Introductory Physics Homework Help
Replies
17
Views
3K
• Introductory Physics Homework Help
Replies
16
Views
1K
• Introductory Physics Homework Help
Replies
14
Views
6K
• Introductory Physics Homework Help
Replies
8
Views
4K
• Introductory Physics Homework Help
Replies
25
Views
1K