First HW - Two firecrackers explode at the same place in the lab

[crazyapeguy]

Homework Statement

1. Two firecrackers explode at the same place in the laboratory and are separated by a time of 3 years as measured on a lab clock.

(a) What is the spatial distance between these two events in a rocket in which the events are separated in time by 5 years as measured on rocket clocks?

(b) What is the relative speed of the rocket and the lab frames?

Homework Equations

? - I am not exactly sure, but, I believe one relevant equation is:
t` = γ (τ - βx)
x` = γ (x - βτ)

The Attempt at a Solution

Trying to find x:

t`/γ = τ - βx

βx = -t`/γ + τ

x = -t`/γ + τ
__________
β



____________________
Thank you so much for any help. This is my first Physics course so if you don't mind could you assume I know literally nothing, like less than an ant?
My problem is I am thinking: what is the velocity? I am really lost/confused

 

[Simon Bridge]

Welcome to PF;
It looks like you have been doing a course in special relativity. You should not be doing that course without a solid grounding in Newtonian mechanics.

If you really know so little, then I'd have to give you all that material again - which would take too long and be expensive. Do you have notes and coursework? A textbook? Perhaps you should review those? You can also peruse the various courses online.

What we can do here is help you with the details.

i.e. special relativity is all about comparing measurements made by different observers who are moving relative to each other.

in the above case - do you know why the observer in the rocket times the explosions at 5y apart when an observer in the lab times 3y only?

The explosions are in the same place in the lab - are they at the same place for the rocket observer?