What is Ann's final position in different reference frames?

[Sanjay87]

Hi,

I'm quite new to relativity and I'm just going through some problems from past exam papers to prepare for an upcoming subject. The following question has me a little stumped:

Betty is at the origin of her frame of reference. At a certain point in time, this also corresponds to the origin of Ann's reference frame. Betty gives Ann the following instructions: walk 1km East, 2km North and 3km East. (there is an x-y graph pictured, indicating that 1km East corresponds to local co-ordinates (1,0) and 1km North corresponds to local co-ordinates (0,1)). The questions are - What is Ann's final position in her own frame? What is Ann's final position in Betty's frame?

Presumably, Ann and Betty are in different reference frames S and S' respectively, with S' moving at constant speed v relative to S.

I hope somebody can help me.

Kind Regards,
George

 

[Antenna Guy]

Betty gives Ann the following instructions: walk 1km East, 2km North and 3km East. (there is an x-y graph pictured, indicating that 1km East corresponds to local co-ordinates (1,0) and 1km North corresponds to local co-ordinates (0,1)). The questions are - What is Ann's final position in her own frame? What is Ann's final position in Betty's frame?

I suspect that Ann's position within her own frame is trivial (since she is the origin of her own frame), but you should note that directions of "East" and "North" generally refer to angular directions on a (presumably) spherical surface.

Regards,

Bill

 

[Mentz114]

Presumably, Ann and Betty are in different reference frames S and S' respectively, with S' moving at constant speed v relative to S.

Why 'presumably' ? If you don't have details of their relative velocities, how can the problem be solved ?

 

[Antenna Guy]

Why 'presumably' ? If you don't have details of their relative velocities, how can the problem be solved ?

heh-heh..

What if Betty told Ann how fast to walk?

I think the relations regarding N/E and x,y imply that Betty and Ann have the same velocity with respect to something infinitely far away.

Then again, if Betty told Ann to change her altitude, there would be a problem...

Regards,

Bill

 

[Sanjay87]

Why 'presumably' ? If you don't have details of their relative velocities, how can the problem be solved ?

This is why the question has stumped me. The way the question is worded, Betty and Ann are in different reference frames which must be moving at some velocity relative to each other, and perhaps they expect the answer to be in the form of variables - e.g. x' = 2+vt. Or have I misunderstood the question (I suspect that I have misunderstood it).

 

[Sanjay87]

Hi again,

Using the Galilean transformations, I would say that in Betty's frame, Ann is at position (-2+vt, 2). But it worries me that no velocity has been given. The response from Antenna Guy makes sense so in that case both parties would agree that Ann is at (-2,2). What do you think?