# Vector, velocity, and parallel

1. Jan 22, 2009

### -EquinoX-

1. The problem statement, all variables and given/known data

A 100 meter dash is run on a track in the direction of the vector v = 4i + 7j. The wind velocity w is 5i + j km/hr. The rules say that a legal wind speed measured in the direction of the dash must not exceed 5 km/hr.

Find the component of w which is parallel to v.

2. Relevant equations

3. The attempt at a solution

I have no idea to solve this problem

Last edited: Jan 22, 2009
2. Jan 22, 2009

### Hootenanny

Staff Emeritus
You must have some idea. Which operation gives to the component of one vector that is parallel to another?

3. Jan 22, 2009

### -EquinoX-

it's parallel to one another if it's angle between them is 0 right?

so therefore using the geometric of vectors:

v . w = |v| * |w|, right?

4. Jan 22, 2009

### gabbagabbahey

Sure, if v . w = |v| * |w| then w and v are parallel; but that's not what Hootenanny was asking.

Suppose you want to find 'the component of w' that is parallel to v....how would you do that?

5. Jan 22, 2009

### Hootenanny

Staff Emeritus
That is correct. However, it is perhaps more useful to note that:

$$\mathbf{v}\cdot\left(\frac{\mathbf{w}}{\left\|\mathbf{w}\right\|}\right) = \left|\mathbf{v}\right|\cos\theta$$

That is, if u is a unit vector then the scalar product v.u gives the projection of v in the direction u.

Edit:
:grumpy:

6. Jan 22, 2009

### -EquinoX-

hmmm...so how do I apply this to the question?

7. Jan 22, 2009

### gabbagabbahey

8. Jan 22, 2009

### -EquinoX-

Is this question asking for a new wind speed/vector which is parallel to v

9. Jan 22, 2009

### Hootenanny

Staff Emeritus
No. The question is asking for the component of w that is parallel to v. Can you use the hints I have you in post number 5 to solve this problem?

10. Jan 22, 2009

### -EquinoX-

No, I don't....

11. Jan 23, 2009

### Hootenanny

Staff Emeritus
I don't know how I can make it clearer without explicitly giving you the answer. Pay particular attention the the last paragraph in on of my previous posts.

12. Jan 23, 2009

### -EquinoX-

what is u related to my question?

13. Jan 23, 2009

### -EquinoX-

why is it v . w/||W|| not w . v/||v||

14. Jan 23, 2009

### gabbagabbahey

v . w/||W|| gives the component of v parallel to w.

w . v/||v|| gives the component of w parallel to v.

Since you are trying to find the component of the wind speed w parallel to the velocity v; you will indeed want to use w . v/||v|| for your problem.

15. Jan 23, 2009

### -EquinoX-

ok thanks! I got it now