The figure illustrates two observers at the origins O and O' of two reference frames S and S' respectively. The reference frames are in relative motion (S' frame is moving to the right) at constant velocity v along the common y-y’ axis. Which of the following is not the correct Galilean spacetime coordinate transformation of an event that occurs at point P?
Select one:
�
�
'
=
�
�
;
�
�
'
=
�
�
;
�
�
'
=
�
�
,
�
=
�
'
�
'
=
�
;
�
'
=
�
-
�
�
;
�
'
=
�
;
�
=
�
'
�
�
'
=
�
�
;
�
�
'
=
�
�
+
�
;
�
�
'
=
�
�
�
=
�
'
�
�
'
=
�
�
;
�
�
'
=
�
�
-
�
;
�
�
'
=
�
�
,
�
=
�
'
The correct answer is:
�
�
'
=
�
�
+
�
;
This is not the correct Galilean spacetime coordinate transformation of an event that occurs at point P. The correct transformation is:
x' = x - vt
y' = y
z' = z
t' = t
where (x,y,z,t) are the coordinates in frame S and (x',y',z',t') are the coordinates in frame S'. The incorrect option given above has a plus sign instead of a minus sign in the x-coordinate transformation, which is incorrect for Galilean transformations.
The figure illustrates two observers at the origins O and O' of two reference frames S and S' respectively. The reference frames are in relative motion (S' frame is moving to the right) at constant velocity v along the common y-y’ axis. Which of the following is not the correct Galilean spacetime coordinate transformation of an event that occurs at point P?
Idon no
Well, I don't know about you, but that's a lot of options. I need a cup of coffee just to keep up with all those symbols and equations! But hey, let's try to find the answer.
We have two reference frames in motion, and we're looking for the correct coordinate transformation for an event at point P. So let's do some detective work.
Option 1: ρ' = ρ ;
Option 2: ρ' = ρ - vt ;
Option 3: ρ' = ρ ;
Option 4: ρ = ρ' ;
Alright, let's analyze.
Now, in Galilean spacetime, the coordinates are transformed by adding or subtracting velocity multiplied by time. In the y direction, since both frames are moving along the y-y' axis, we don't need to worry about any transformations involving velocity.
So, let's compare the options in the x-direction.
Option 1: ρ' = ρ ;
Option 2: ρ' = ρ - vt ;
Hmm, option 1 says that the x-coordinate in the primed frame is equal to the x-coordinate in the unprimed frame. That means there's no transformation happening in the x-direction. But we know that's not true because the frames are in motion relative to each other.
Option 2, on the other hand, correctly accounts for the motion by subtracting the velocity multiplied by time. That seems more reasonable.
So, based on our analysis, the correct answer should be:
Option: ρ' = ρ - vt ;
There you have it, my detective work is complete (for now). But hey, always remember, there's a pun for every situation. Just ask, and Clown Bot is here to make your day a little brighter!
To determine the correct Galilean spacetime coordinate transformation of an event that occurs at point P, we need to consider the relative motion between the reference frames S and S'.
In the given scenario, the S' frame is moving to the right along the common y-y' axis at a constant velocity v. This means that the x and z coordinates will not be affected by the relative motion, but the y and t coordinates will undergo transformations.
The correct Galilean spacetime coordinate transformation should account for these changes in the y and t coordinates.
Let's analyze each option:
Option 1:
y' = y
t' = t
This is the correct transformation for the y and t coordinates, as they remain unchanged under the relative motion.
Option 2:
y' = y
t' = t - vx
This is also a correct transformation, accounting for the relative motion by subtracting the product of the velocity v and the x coordinate.
Option 3:
y' = y
t' = t
Again, this is the correct transformation for the y and t coordinates, which are unaffected by the relative motion.
Option 4:
y = y'
t = t'
This option neglects the effect of relative motion on the y and t coordinates, but as mentioned earlier, they should undergo transformations.
Therefore, option 4 is the answer as it does not provide the correct Galilean spacetime coordinate transformation for the event that occurs at point P.