# 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?