1. ## Relative velocity question

Lets say if I have particle P with velocity Vp which is intercepting another particle Q with velocity Vq. For the particles to intercept, should the velocity of P relative to Q (Vp-Vq) always be pointing towards Q? My textbook says:

We 'fix the target' by applying the vector -Vq to Q, but we must also apply this vector to P as well, ending up with Vp-Vq= pVq, which points towards the position of Q when it is stationary.

2. ## Re: Relative velocity question

I am not understanding your notation. Do you have a specific example they give? Specifically, what does $pVq$ mean? You have a point $P$, and a velocity $V_p$, but you do not have a value $p$. Is that a scalar or vector? How many dimensions are you working with? This question is obviously much easier to answer in two dimensions than it is in three. What do you mean by "intercept"? What type of particle collisions are you working with? Are there glancing collisions? Or after an "interception", do you have two particles acting as one (sort of a fusion of the two)?

3. ## Re: Relative velocity question

pVq means the velocity of P relative to Q.
We are working in two dimensions
By intercept, we are just talking about whether they would meet in their trajectories. I really do not understand the stuff they said in the second picture Why did they just reduce the velocity of Q to 0 and add its vector onto P? Please could you, if possible, explain it in layman terms as I've been trying to make sense of this for ages!

4. ## Re: Relative velocity question

Originally Posted by bindra

pVq means the velocity of P relative to Q.
We are working in two dimensions
By intercept, we are just talking about whether they would meet in their trajectories. I really do not understand the stuff they said in the second picture Why did they just reduce the velocity of Q to 0 and add its vector onto P? Please could you, if possible, explain it in layman terms as I've been trying to make sense of this for ages!
Imagine empty space where there are no points of reference. You have two particles moving around. To the observer outside the system, we can observe the two particles moving around. Suppose you were sitting on one of the objects. To you, you have no frame of reference to determine if you are moving or not. Your only frame of reference is the other particle. You watch the other particle move with respect to you, but as far as you are concerned, you are at rest while sitting on your particle. Since you cannot view the whole system, but only your reference from your perch atop your one particle, you cannot see that you, too, are moving.

Now, add in the rest of the world. You now have more frames of reference. But, you remember that feeling of being "stationary". Now, you watch the world zipping by you. Is it you that is moving? Or is it the world moving beneath you? So long as you use a consistent frame of reference, physics does not care which reference you use. The math will work out every which way. This example was showing you that.