# Lorentz transformations

1. Sep 21, 2010

### DarkMalice

Anyone help. I know I must be doing this wrong somehow

Lightning hits both a tree and a pole. The spacetime coordinates for each is (x=0, t=10us) for the tree and (x=30000m, t=10us) for the pole relative to the ground. Therefore they occur simultaneously relative to the ground. A rocket comes whizzing by at 0.5c in the x-direction. Find the spacetime coordinates relative to the rocket. Do the events happen simultaneously in the rocket's frame? (us is microseconds by the way)

First and foremost, I was able to find the factor y as y= 1/(1-.05^2)^.5 = 1.1547

Using Lorentz transformations
For the tree
x'= 1.1547 X [0 -(0.5c)(10us)]
= -1732.05m

t'=1.1547 X [10us -(0.5c)(0)/c^2]
= 11.547us

For the pole
x'= 1.1547 X [30000-(0.5c)(10us)]
= 32908.95

t'= 1.1547 X [10us - (0.5c)(30000)/c^2]
=-46.18us

What I want to know is why is x'(pole)-x'(tree)> 30000? Shouldn't the distance between both poles go through length contraction in the rocket's frame and therefore be shorter than 30000?

Please someone help

2. Sep 22, 2010

### vela

Staff Emeritus
You're comparing the location of the tree and the location of the pole at different times in the rocket's frame. To find the distance between the two, you need to compare where they are at the same time.

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