# B Difference between relative velocity and effective velocity

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1. Dec 28, 2017

### Abhimessi10

Can anyone tell me the difference between concept of relative velocity and effective velocity and when to use the concept of relative velocity?

For example, if a guy throws a ball from a moving object at an angle theta it undergoes projectile motion we write horizontal velocity as ucostheta+v(effective velocity)why not ucostheta-v(relative velocity)

Last edited by a moderator: Dec 29, 2017
2. Dec 29, 2017

### kuruman

First you decide what reference frame to use, then you consider the velocity relative to the chosen frame. As long as you are consistent and refer all velocities to the chosen frame, you are OK. For example, suppose the guy is standing on a boat in a river moving with speed vbw relative to the water and the water is moving with speed vws relative to the shore. Now if the guy throws a rock and he sees it move away from him with speed vrg, there many velocities that the rock has depending on the frame in which yo want to express it.
Relative to the guy (or the boat), the rock has velocity vrg.
Relative to the water, it has velocity vrg+vbw.
Relative to the shore, it has velocity vrg+vbw+vws.
Relative to the center of the Earth, it has velocity vrg+vbw+vws+vsc, where the last term is the speed of the surface relative to the center of the Earth.
You can similarly calculate the velocity of the rock relative to the Sun, relative to the Milky Way or relative to a Galaxy far far away. You see how it goes. All velocities are relative velocities and you need to be clear what they are relative to, i.e. the frame of reference you have chosen to express them in.

As far as effective velocity is concerned, I didn't know what it was and looked it up. I found this link
http://probaseballinsider.com/effective-velocity-what-is-it-how-is-it-used-how-can-it-help-pitchers/
where it is stated that effective velocity (in baseball) is a combination of two things, (a) A hitters perceived velocity and (b) How far a hitter has to move his bat to make contact. In my opinion this definition is a statistical concept that may be useful in baseball but not in physics because item (a) is subjective and depends on the hitter while item (b) is an attempt to define this velocity as distance-dependent which adds to the fuzziness of the concept.

3. Dec 29, 2017

### PeroK

You need to define $u$ and $v$ here.

4. Dec 29, 2017

### Abhimessi10

So

5. Dec 29, 2017

### kuruman

As @PeroK remarked you need to define $u$ and $v$. They represent velocities relative to what? Also, how do you understand "effective velocity"? If your problem is with signs, i.e. when one uses plus as opposed to minus, remember that velocity is a vector and can be positive or negative. If the boat is moving to the right (positive) relative to the water and the guy throws the rock forward (also positive), then the velocity of the rock relative to the water will be vrw = vrg+vbw. If the guy throws the ball backwards (negative) then vrw = -vrg+vbw.

6. Dec 29, 2017

### Abhimessi10

By effective velocity I mean resultant velocity
After I saw some videos I think that effective velocity is just another case of relative velocity which would depend on the frame of reference as you said

Last edited: Dec 29, 2017
7. Dec 29, 2017

### kuruman

OK, I see. Exactly what velocity you mean would be clearer if you stopped using the word "effective" or "resultant" and started using words or subscripts that clearly specify the frame of reference to which your velocity is referred as I did in post #2.

8. Dec 29, 2017

### Abhimessi10

If you don't mind you I could give the link to
the question (video)

9. Dec 29, 2017

### PeroK

Let me help.

In the ground reference frame an object is moving with velocity $v$ horizontally.

That object fires a projectile with speed $u$, angle $\theta$ relative to itself - i.e in its frame of reference.

What is the velocity of the projectile in the ground frame? I.e the resultant or effective velocity.

10. Dec 29, 2017

### Abhimessi10

He is talking about relative velocity of the ball with respect to ground right ?(ucostheta+v)

11. Dec 29, 2017

### PeroK

I can't see the video, but that makes sense. The velocity of the ball in the ground frame is:

$(v+u\cos \theta, u \sin \theta)$

12. Dec 29, 2017

### Abhimessi10

So while solving questions how do you choose the frame of reference?

13. Dec 29, 2017

### PeroK

You choose the frame of reference that you think will make the problem easiest to solve. This is usually obvious but sometimes a clever change of reference frame make the problem much simpler to solve.