# Solving Addition of Vectors Problem: Peter G's I.B Physics High Journey

• Peter G.
In summary, the conversation discusses a physics problem involving a bird flying with a steady velocity and a wind blowing in a different direction. The problem asks for the resultant velocity and displacement, but the question is confusing. The expert suggests drawing a sketch and using trigonometry to find the answer. The conversation ends with the clarification that the bird needs to fly towards the north and a little west to counter the wind.

#### Peter G.

So, I started my I.B Course for Physics High and we've took off with a simple subject, addition of vectors. We finished it today but the last question was quite hard. I had a try, asked the teacher but the thing is I can't understand what the problem asks for, or how to approach the problem:

A bird flies at a steady speed of 3 m/s through the air. It is pointing in the direction due north. However, there's a wind blowing from west to east at a speed of 2 m/s. It then asked for the resultant velocity and displacement which I handled with no problem and finished off with: In what direction should the bird point if it is to travel in a northerly direction?

So, firstly: By northerly, should the resultant velocity direction be bearing 0? Like, straight line, north? Or the bird should move towards the north direction?

So, the teacher put the answers up the board so after I had a try I looked. From the answer, I managed to reproduce the diagram obviously and identify the angle but I still don't understand the question itself

Sorry, I don't know how to post up the picture but in case you guys find it helpful:
tap.iop.org/mechanics/statics/file_39599.doc

Last question, both answer and question available.(3)

Peter G.

I think the problem is the problem. I mean, the problem is a bit confusing. It asks for displacement, but we are only given two velocities. One can get the resultant velocity, which I hope you know how to do, but one can't get a displacement, only a rate of displacement (which is just velocity).

So ignoring the question of displacement, determining the resultant velocity you know how to do. The second part is almost the same. Now the resultant velocity must face north. The bird must fly north and a little west, to counter the effect of the wind. How much west must the bird fly? Just enough, that is the clue. Draw a sketch, put in the magnitudes and use your knowledge of trigonometry to find the answer.

Ah, ok, so the resultant velocity is towards north. For example (this will be a bit confusing). The counter effect of the wind will be 2ms west. I draw one arrowed line towards my left. I draw a North Line, upwards (my resultant direction) and join a 3ms line from the 2ms line to the North line.

Yeah, to know the displacement we would need to know for how long he flew and multiply by our resultant velocity.

Thanks,
Peter G

You got it. Then draw an accurate scale diagram to measure the angle or use trigonometry, whichever is easier. The answer would be something like 20 degrees W of N, or whatever.

Dear Peter,

Congratulations on starting your I.B Course for Physics High! Addition of vectors is a fundamental concept in physics and it is great that you are already tackling it. It is common to encounter challenging problems in physics, but with determination and guidance, you will be able to solve them.

To answer your question, the resultant velocity in this problem should be pointing in the northerly direction, which means it should have a bearing of 0 degrees. This means that the bird should be moving towards the north direction. The resultant velocity is the combination of the bird's steady velocity of 3 m/s due north and the wind's velocity of 2 m/s from west to east. The direction of the resultant velocity is important because it determines the bird's overall motion.

In order to find the direction the bird should point in order to travel in a northerly direction, you need to consider the angle between the resultant velocity and the bird's original velocity. In this case, the angle would be 30 degrees, as shown in the diagram provided. This means that the bird should point 30 degrees west of north in order to travel in a northerly direction.

I understand that it may be confusing to understand the question and the concept at first, but with practice and asking for clarification when needed, you will get a better grasp of it. Keep up the good work and don't hesitate to ask your teacher or fellow classmates for help when needed.

Best of luck with your physics journey!

Sincerely,

## 1. What is the process for solving addition of vectors problems?

The process for solving addition of vectors problems involves breaking down the vectors into their horizontal and vertical components, adding the respective components separately, and then using the Pythagorean theorem to find the magnitude and the inverse tangent function to find the direction of the final vector.

## 2. How do I know when to add or subtract vectors?

You add vectors when they are acting in the same direction and subtract them when they are acting in opposite directions. You can determine this by looking at the direction of the arrows representing the vectors. If they are pointing in the same direction, you add them; if they are pointing in opposite directions, you subtract them.

## 3. What are the key formulas needed to solve addition of vectors problems?

The key formulas needed are the Pythagorean theorem (a² + b² = c²) for finding the magnitude of the final vector and the inverse tangent function (tan⁻¹) for finding the direction of the final vector. Additionally, you may need to use trigonometric functions like sine, cosine, and tangent to find the components of the vectors.

## 4. How do I handle vectors at angles other than 0, 90, or 180 degrees?

To handle vectors at angles other than 0, 90, or 180 degrees, you will need to use trigonometric functions to find the components of the vectors. You can use sine and cosine to find the horizontal and vertical components respectively, and then use the Pythagorean theorem and inverse tangent function to find the magnitude and direction of the final vector.

## 5. Can you provide an example of solving an addition of vectors problem?

For example, if we have two vectors A and B with magnitudes of 5 and 3 respectively, and angles of 30 and 45 degrees, we can use trigonometric functions to find their horizontal and vertical components. A will have a horizontal component of 4.33 and a vertical component of 2.5 while B will have a horizontal component of 2.12 and a vertical component of 2.12. Adding these components separately, we get a horizontal sum of 6.45 and a vertical sum of 4.62. Using the Pythagorean theorem, we can find the magnitude of the final vector to be 7.77 and using the inverse tangent function, we can find the direction to be 32.4 degrees.