- #1
affans
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Homework Statement
A light signal is sent from the origin of a system K at t = 0 to the point x = 1 m, y = 8 m, z = 13 m. a) At what time t is the signal received?
b) Find ( x', y', z', t' ) for the receipt of the signal in a frame K' that is moving along the x-axis of K at a speed of 0.6c.
Homework Equations
The lorentz transformations:
x' = [tex]\gamma * (x - vt)[/tex]
y' = y
z' = z
The Attempt at a Solution
Part a was easy. I got the right answer. I just took the length of the vector given by the co-ordinates and divided by the speed of light. The answer is [tex] 5 * 10^8 [/tex] I am having trouble with part b.
Ofcourse, y' and z' were easy to get. t' (i had 3 tries, and i used them all) so I lost a mark there. I have one try left on x'.
Using the equation, we first have to solve for [tex]\gamma[/tex]. Plugging the numbers into the equation for gamma:
[tex] \frac{1}{\sqrt{1-(v/c)^2}}\; \text{yields} \; 1.25[/tex]
Then using the lorentz transformation I have the following eqn:
x' = [tex]\gamma[/tex] (x - vt) . Plugging in the numbers yeilds
x' = 1.25(1 - 0.6 * c *(5E-8))
I get 10 as the answer. It is wrong. I also thought t = 0 could work since that's when the event happened. But the answer 1.25 is also wrong.
My third attempt yielded 11.25m however, I am scared to submit it. If anyone can please verify my number for me.