Addition of 2-D vectors and relative velocity

In summary, the conversation discusses the direction a plane must point in order to reach a destination located due north from its departure point, given a gentle wind blowing from the south-west. The solution involves considering the displacement in two different situations and finding the correct components to reach the desired destination.
  • #1
Bruce_Wayne
1
0

Homework Statement



A plane must fly to a destination located due north from its departure point. A gentle wind is blowing from the south-west. What direction must the plane point to reach its destination?

Homework Equations





The Attempt at a Solution



http://i.minus.com/iMPPjrIF6APd.png


In situation 1 I drew the displacement if the plan was to fly due north. In situation 2 I drew the displacement if the plane was to fly north-west.

I'm not really sure, but I think that sit. 2 might be what happens if the plane wanted to reach its destination.
 
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  • #2
You have the geometry right, now you just need get the components to work out. Without a little more info, there's not much more we do.
 

Related to Addition of 2-D vectors and relative velocity

1. How do you add two-dimensional vectors?

To add two-dimensional vectors, you must first identify the x and y components of each vector. Then, simply add the corresponding components together to get the resultant vector. For example, if vector A has components (2,3) and vector B has components (1,4), the resultant vector would be (2+1, 3+4) or (3,7).

2. What is the formula for calculating the magnitude of a vector?

The formula for calculating the magnitude, or length, of a vector is √(x² + y²), where x and y are the x and y components of the vector, respectively. This formula is derived from the Pythagorean theorem.

3. How do you find the direction of a vector?

The direction of a vector can be found using trigonometry. The angle of the vector can be determined by taking the inverse tangent of the y component over the x component. This will give you the direction in terms of degrees or radians.

4. What is relative velocity?

Relative velocity is the velocity of an object in relation to another object. It takes into account the motion of both objects and is often used in scenarios where two objects are moving in different directions or at different speeds.

5. How do you calculate relative velocity?

To calculate relative velocity, you must first determine the velocities of both objects. Then, you can use vector addition to find the relative velocity by adding the velocities of the two objects together. This resulting vector will represent the relative velocity between the two objects.

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