Mechanics

Take up skeet shooting, and you will learn all about this.

Face East. Hold a ball in your left hand. Toss it to your right hand, and catch it.

There now. What did you find out about the speed of the ball compared to the speed of your left or right hand?

Does it matter that the ball made a small arc in traveling from left to right (north to south)? If that arc does matter, then use a laser pointer held in your left hand and aimed at your right hand. (The photons will also make a tiny arc, but not one you could likely ever detect.)

Is one of these bodies riding a bike?

As you see the speed depends on the transverse distance and meeting point distance.

If distance D is covered in T seconds at the spead of V1 and projectile also reaches from one body to other in T seconds then following way V1 and V2 can be related:

TxV2 = [ (TxV1)**2 + L**2 ]**1/2

What' s the difference between what I wrote and your comment ? Is your comment some thing new ?

What 's the difference between what I wrote and your comment ? Is your comment something new ?

You seem annoyed at Pritam's comment. Why? You are not the only one allowed to make an algebraic comment. Besides, if you look closely, you'll see his answer is not identical to yours.

And by the way, your answer may not be correct. The question allows for the possibility that V2 is actually the vector you show labeled as Vt (i.e., the velocity V2 is orthogonal to V1). In which case the vector equation would be V2 = Vt - V1, rather than your answer V2 = Vt + V1.

In point of fact, V1 and V2 can be completely independent of each other.

Dear Sir,

You are completely wrong ! I am not annoyed at all but in my humble opinion a new answer should bring a new idea. This was the reason for my question assuming that in my poor and narrow mind I could not see what was new.

Your aggressive comment is, again on my humble opinion, quite curious. I may if you will allow it explain why. In fact any velocity Vt will lead to a meeting of trajectories but not always to the expected bodies meeting. You are of course right that V1 and V2 are independent from each other but only a defined relationship allows a meeting where this meeting is wished. Of course I could make the error to assume that in general a meeting is wished and not only a crossing of the 2 paths. This was the reason why I connected the speeds to the position where the meeting would take place.

As was noticed the "emission" of a mass from body 1 and the "reception" of same mass by body 2 will have an influence of the speeds as well in direction of V1 as in the transversal one (Vt). This influences are function of the impulse of the small mass = m*V2 with respect to the main impulse M*V1.

Further relative to your interpretation the 2 answers are in fact identical since in both cases times are equal the difference is only what was considered as more important parameter. Since the time is always the same I repeat that I considered more important to refer to the meeting point.

May I also remind you - as far as I am not wrong, what I always can be- that operations with velocities (+ or -) have to be done in a vectorial form what you unfortunately either have forgotten or neglected. In both cases I would strongly recommend to take again a book about kinematics and have a look. May I mention that such a situation is normally analysed using the principle of relative and absolute references.

If my explanations are not comprehensible or too short I am always at your disposal for a deeper and broader one.

Apparently you are unfamiliar with advanced Physics notation. When I said 'The vector equation' and wrote the symbols in boldface type, that was a clue (to people who understand such things) that this is vector addition. Roger Penrose uses this technique, for example, in his book "The Road to Reality; a Complete Guide to the Laws of the Universe". Misner, Thorne and Wheeler used the same notation in their famous book "Gravitation".

And in fact your latest 'explanation' merely muddied the waters. It was a given in the OP that a substance was projected from one body to the other; it made no sense for you to say "any velocity Vt will lead to a meeting of trajectories but not always to the expected bodies meeting". Completely pointless. As was your discussion of masses. Nowhere in the OP was the subject of masses or momenta raised.

As I wrote in my simple and narrow minded way of thinking I was not able to appreciate your high level notation. I agree you are at the top and I am at the bottom, satisfied ?

In fact your reaction shows a peculiar way of thinking, you assume that what you use as source is the ONLY one possible in the world. Could this not be a bit arrogant ?

Notations are different from country to country and it would have been better since not all CR4 members are at your high level to indicate that bold notation means vector. But of course you cannot imagine this from the mountain peak ants are not seen, isn't it ?

I am surprised that taking into account your high level references you did not consider the contraction factor and mentioned it. I expected more from some body who reads so impressive books

With respect to last part of your comment, if you read the comment before yours the problem was mentioned so that it made sense to take care of this aspect. And I not wrong any transversal speed will lead to a trajectories crossing if of course this transversal velocity is not =zero. Is that soo wrong?

In fact you lost your temper this is clear in the way you reacted. Not good for your health.

Dear Nickname,

Not at all. In fact, before posting my comment I missed to see the equation (in faded font) you have given at top. As OP wanted relation between V1 & V2, I tried to extend it from your explanation.

I asked as mentioned before by curiosity. It was not any attack against you. Unfortunately some of our colleagues want to defend when it is not necessary and become aggressive at first and insulting later when they have no other arguments. Please do not take the wrong way my question it was not my intention.

wrong...the vehicle from which the object was projected will slow down relative to the force it took to project the projectile and the receiving vehicle will be speeded up by the force of the object relative to it's density and speed unless it is a liquid.

Speed with respect to what reference of frame?

Do I take the bodies as frame of reference?

NOTE-1- the two bodies are moving with equal speed and not velocity, parallel to each other (so two different relative velocities are possible. Are we assuming the Velocity for speed?

NOTE-2- I would have assumed that in CR4 we allow one to do their homework themselves? The framing of the question looks suspiciously like homework and we are not only giving all the vector diagrams but the calculations too?

Note-3. The above calculations will be answer one of the four possible (I would say probable) scenario assuming the professor meant the reference frame to be either

(a)the base (with reference to which the two objects are moving) or

(b) the object from which the projectile is thrown.

Else- possibilities are infinite.

NOTE-4 OP we usually use u for speed and v for velocity. _{(Unable to put the vector symbol in available characters in the editor)}