• Support PF! Buy your school textbooks, materials and every day products Here!

Lorentz transformation problem

208
0
1. Homework Statement
A spaceship has a speed of .8c relative to Earth. In its own reference fram, the length of this spaceship is 300m.
a.) consider a light emiited from the tail of this spaceship. In the reference frame of the spaceship, how long does this pulse take to reach the nose>
b.) In the reference frame of the Earth, how long does this take? Calculate this time directly from the motions of the spaceship and the light pulse; hen recalculate it by applying the Lorentz transformations to the result obtained in (a).

2. Homework Equations
[tex] t =\frac{t' + \frac{Vx'}{c^{2}}}{\sqrt{1-\frac{V^{2}}{c^{2}}}}
[/tex]


3. The Attempt at a Solution
I think i have part a figured out.. All i did was divide 300 by c to get [tex] \Delta t' = 1.0*10^-6s[/tex]

b.) For this part, I cannot figure out how to do it without using the Lorentz transform directly like so:
[tex]t' = 1.0*10^-6s........
x' = 300m........
V = .8c
[/tex]

[tex] t =\frac{1.0*10^-6s + \frac{.8c(300m)}{c^{2}}}{\sqrt{1-\frac{(.8c)^{2}}{c^{2}}}}
= 1.40 * 10^-6s [/tex]

I cannot do this though without the lorentz transform. We haven't gone over length contraction yet, so I cannot use it to determine the length of the spaceship in earths reference frame. If anyone could please help me get started on this I would appreciate it greatly!
 
Last edited:

Answers and Replies

208
0
I've been trying to manipulate the other lorentz equations ( in specific the ones for x), but i cannot find anything that will work. Once again, If someone could help me out here I would appreciate it
 

Related Threads for: Lorentz transformation problem

  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
4
Views
700
  • Last Post
Replies
4
Views
4K
  • Last Post
Replies
0
Views
1K
Replies
1
Views
3K
  • Last Post
Replies
0
Views
838
  • Last Post
Replies
2
Views
839
Top