Special Relativity and Space-Time Diagrams

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Homework Statement

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S' is moving at 0.5c relative to S.

Two events, stationary with respect to S, occur at a distance of 4 light years from the origin at time 3 years and 6.5 years. Estimate the time between the events as measured by an observer in S'. Check your solution with the time dilation formula.

Homework Equations

Time dilation: γ=ΔT / ΔT₀

Since v=0.5c, then γ = 1.155

The Attempt at a Solution

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I first placed the points for the two events at the coordinates (4, 3) and (4, 6.5) on the space-time diagram with the grid that corresponds to the reference frame of S. If I then see what the y-axis readings are for the reference frame of S', I get 1.0 years and 5.0 years. Therefore, the time between the events according to S' must be 4.0 years.

Since S is stationary with respect to the two events, then ΔT₀ = 3.5 years.

3.5 * 1.155 = 4.0 years

I'd like some verification if I did this correctly. Any help is greatly appreciated. Thanks!

 

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Can you show your sketch?

I'd like some verification if I did this correctly.

You can use the time-dilation formula as cross-check. It is part of the problem anyway.

 

[Jefffff]

Can you show your sketch?You can use the time-dilation formula as cross-check. It is part of the problem anyway.

Yep, here's a photo. The dots I've drawn are in blue.

 

[mfb]

Looks fine.