Special relativity relating 3 dimensions

[Eats Dirt]

Homework Statement

An event happens in frame S at x=100m y= 10m z=1m at time t=2*10^-3s. What are the coordinates of this event in rame S' that is moving with velocity v=0.92c (ihat) and the orgins coincide at time t=0.

Homework Equations

Lorentz transformations

The Attempt at a Solution

I would think to do length contraction just in the x-axis but I don't think that is right.
Im not entirely sure how to boost from S to the frame S"

 

[Chestermiller]

Homework Statement

An event happens in frame S at x=100m y= 10m z=1m at time t=2*10^-3s. What are the coordinates of this event in rame S' that is moving with velocity v=0.92c (ihat) and the orgins coincide at time t=0.

Homework Equations

Lorentz transformations

The Attempt at a Solution

I would think to do length contraction just in the x-axis but I don't think that is right.
Im not entirely sure how to boost from S to the frame S"

Why don't you just use the straight Lorentz Transformation equations?

 

[Eats Dirt]

Why don't you just use the straight Lorentz Transformation equations?

Which ones?
x'=y(x-Bct)?

 

[Chestermiller]

Which ones?
x'=y(x-Bct)?

Yes. But you can also use the other LT equation to give you the t' coordinate of the event.

 

[Nickie]

that is moving with velocity v=0.92c (ihat) and the origins coincide at time t=0.

To solve this problem, we can use the Lorentz transformations, which relate coordinates and time between two frames of reference moving at a constant velocity relative to each other. We can use the Lorentz transformations for the x, y, and z coordinates separately.

For the x-coordinate, we have:

x' = γ(x - vt)

Where γ is the Lorentz factor, given by γ = 1/√(1 - v^2/c^2) and v is the velocity of frame S' relative to frame S.

Substituting in the values given in the problem, we have:

x' = (1/√(1-0.92^2)) * (100m - 0.92c * 2*10^-3s)

x' = 245.9m

Similarly, for the y-coordinate, we have:

y' = y

Substituting in the given value of y, we have:

y' = 10m

And for the z-coordinate, we have:

z' = z

Substituting in the given value of z, we have:

z' = 1m

Therefore, the coordinates of the event in frame S' are x' = 245.9m, y' = 10m, and z' = 1m.