# Observers and velocity

Hi everyone, i dint post this i homework section because i know how to solve the problem.
So here is a problem

Two objects are moving at the same line in different directions i.e. toward each other, with speeds 2*10^5 km/s(relative to the standing observer). What is the speed of one body relative to the other, calculate by classical laws and by relativistic laws of velocity-addition.
So i am standing and in my own reference system S i observe two objects moving toward each other at speed 2*10^5 km/s each. Object in it's own reference system S' is observing object moving toward him at speed 2*10^5 km/s and it's own S' is moving with speed u(relative to S) is moving object 2, and object 2 in it's own reference system S'" is also observing object moving toward him at speed 2*10^5 km/s and it's own S'' is moving with speed u(relative to S).

So to think of this problem in another way lets say i am in a car with speed u1=2*10^5 km/s moving toward another car with speed u2= 2*10^5 km/s. Speed of that second car relative to me is should be q=u1+u2= 4*10^5km/s. That is by classical laws but by relativistic laws it should be V'=(u1+u2)/(1+ (u^2)/(c^2)). Where u1 is speed of my car relative to standing observer and u2 speed of second car relative to my reference frame. Also i think that it is + between u1 and u2 since we are moving in opposite directions. Then the difference is V-V' and that's that. Problem arises when i asked my teacher a question "In whose reference frame are we calculating these speeds" and she said "In reference frame of standing observer."

This is weird to me because if i am in a car 1 i should detect car 2 traveling at speed u1+u2=
4*10^5km/s and how can that observe standing observer? Should he be able to detect only speeds of car 1 and 2 and only that or also relative speed of car 1 and car 2. My "logic" says to me that it can only detect speeds of car 1 and car 2. Also in my text book they wrote solution with V' and i guess that V' is reserved for S' system that is moving and S that is standing and only observing.

I hope you understand my question i tried to write this as clearly as possible.

Thank you

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All observers agree on the relative velocity between two objects. What you deduce the relative velocity to be using the velocity addition formula is exactly what car 1 perceives car 2's velocity to be.

All observers agree on the relative velocity between two objects. What you deduce the relative velocity to be using the velocity addition formula is exactly what car 1 perceives car 2's velocity to be.
So what are you saying is that observers dont agree on space, velocity, time, lenght but they do agree on relative velocity between two objects?

Also are you saying that formula V'=(u1+u2)/(1+ (u^2)/(c^2)) where u1 is speed of car 1 relative to standing observer and u2 speed of second car relative to car 1, is legit way to find speed of car 2 relative to car one(when the are young at different directions). Also since all observers agree on relative speed of two objects i can use same formula only where u1 is car 1 speed and u2 car 2 speed?

Thank you

So what are you saying is that observers dont agree on space, velocity, time, lenght but they do agree on relative velocity between two objects?
Yes, that is correct.

Also are you saying that formula V'=(u1+u2)/(1+ (u^2)/(c^2)) where u1 is speed of car 1 relative to standing observer and u2 speed of second car relative to car 1, is legit way to find speed of car 2 relative to car one(when the are young at different directions). Also since all observers agree on relative speed of two objects i can use same formula only where u1 is car 1 speed and u2 car 2 speed?
$u_1$ and $u_2$ are speeds of the cars relative to you. The formula gives speeds of either car relative to the other car.

Yes, that is correct.

$u_1$ and $u_2$ are speeds of the cars relative to you. The formula gives speeds of either car relative to the other car.
You mean $u_1$ and $u_2$ are speeds of the cars relative to me when i am calculating relative speeds between cars in S reference system.

You said you were standing still in the S reference frame, so yeah.

You said you were standing still in the S reference frame, so yeah.
Thank you very much.