Calculating unit vector for velocity

In summary, John is trying to calculate the unit vector for velocity, but if he calculates it by angle change, the velocity becomes infinite. He needs to use the dot product of the unit vectors to calculate the velocity.
  • #1
andykol
9
0
Hello,
I am trying to calculate unit vector for velocity (vel= (U*Unit vector)/unit vector). But if I consider calculation by angle change e.g. unit vector= cos(theta) at certain angle velocity becomes infinity.
Please inform me how I can take care of this problem.
Thanks in advance.
 

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  • #2
vel= (U*Unit vector)/unit vector).

This equation makes no sense.

unit vector= cos(theta)

This equation makes even less sense...as cos(theta) is a scalar not a vector.

Typically you make unit vectors by normalizing them, which means to divide by the length.
 
  • #3
The unit vector for velocity would be:
[tex]U=\left(\frac{V_x}{|V|},\frac{V_y}{|V|},\frac{V_z}{|V|}\right)[/tex]

where the magnitude of the velocity vector is given by:

[tex]|V|=sqrt(V_x^2+V_y^2+V_z^2)[/tex]

and

[tex]V_x[/tex],[tex]V_y[/tex],[tex]V_z[/tex], are the [tex]x[/tex], [tex]y[/tex], and [tex]z[/tex] components of the velocity vector respectively.

However, without more information on the original problem I'm not sure if this is what you want.
 
  • #4
Thanks for reply.
I am trying to multiply velocity with unit vector to transfer velocity without calculating at perticular location. Please see attached picture. Please tell me if I m using right equation and its values.

John,
I need to use following equation to calculate velocity for 2D?

[tex]Unit vector=\left(\frac{U_x}{|U|}+\frac{U_y}{|U|}\right)[/tex]

[tex]|U|=sqrt(U_x^2+U_y^2)[/tex]

Then I can calculate U' by (U(x,y)*Unit vector(x,y))/unit vector(x,y)
 

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  • #5
andykol said:
Thanks for reply.
I am trying to multiply velocity with unit vector to transfer velocity without calculating at perticular location. Please see attached picture. Please tell me if I m using right equation and its values.

John,
I need to use following equation to calculate velocity for 2D?

[tex]Unit vector=\left(\frac{U_x}{|U|}+\frac{U_y}{|U|}\right)[/tex]

[tex]|U|=sqrt(U_x^2+U_y^2)[/tex]

Then I can calculate U' by (U(x,y)*Unit vector(x,y))/unit vector(x,y)

I think what you want is the dot product. The dot product will give you the component of the velocity in the direction of the unit vector.

For a unit vector u the projection of V on U is given by:

[tex]Proj_UV=U\cdot V=UxVx+UyVy+UzVz[/tex]
 
  • #6
means-
If we consider one direction like picture I have attached in last post.
U- Velocity(known)
U'-Velocity(unknown)
Uv-Velocity Vector

Then if I am transferring velocity value

U'=U.Uv

Where [tex]U_v=\left(\frac{U}{|U|}\right )[/tex]

But this becomes U'=U. I think this is wrong as location of velocity changes.
 
  • #7
andykol said:
means-
If we consider one direction like picture I have attached in last post.
U- Velocity(known)
U'-Velocity(unknown)
Uv-Velocity Vector

Then if I am transferring velocity value

U'=U.Uv

Where [tex]U_v=\left(\frac{U}{|U|}\right )[/tex]

But this becomes U'=U. I think this is wrong as location of velocity changes.

To make your posts more clear, use subscripts for components of vectors. Now reread my last two posts. As far as I understand your problem, you are trying to find the component of the velocity in the direction of the unit vector. This is not the same thing as finding the velocity.
 
  • #8
Thank you John. This helped alot.
 

1. How do you calculate the unit vector for velocity?

To calculate the unit vector for velocity, you must first find the velocity vector, which is the magnitude and direction of an object's motion. Then, divide the velocity vector by its magnitude to get the unit vector, which represents the direction of the motion in a normalized form.

2. What is the purpose of calculating the unit vector for velocity?

The unit vector for velocity is used to represent the direction of an object's motion without considering its speed. This is useful in many physical and mathematical calculations, such as determining the direction of acceleration or finding the components of a vector in a specific direction.

3. Can the unit vector for velocity have a negative value?

No, the unit vector for velocity is always positive. It represents the direction of motion, not the magnitude of the motion. Therefore, the unit vector for velocity will always have a magnitude of 1 and a positive direction.

4. How do you represent the unit vector for velocity mathematically?

The unit vector for velocity is represented mathematically by placing a hat (^) symbol on top of the velocity vector. For example, if the velocity vector is represented as v, the unit vector for velocity would be v^.

5. Can the unit vector for velocity change over time?

Yes, the unit vector for velocity can change over time if the direction of an object's motion changes. This is because the unit vector represents the direction of motion at a specific point in time. If the direction changes, the unit vector will also change to reflect the new direction of motion.

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