Relativity Help: Finding Distances, Angles & Perimeters

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1.-Two particles moving in a straight line in a laboratory reference system at a speed v = 3/4c, hit a stationary target with a time interval t = 50 [ns]. Finding the proper distance between the particles before hitting the target.

2.-Certain particle moving with velocity v in a sitema O; its direction forms an angle μ with the axis X. To determine the corresponding angle in the system X´ which moves with velocity V over the system or in the positive direction of X axis if the X and X´ match.

3.-There is a triangle where the length of each one of its sides is equal to Lo. Calculate the perimeter of this triangle in a reference system moving with constant with V respect to the over:
a) one side;
b) one of its bisectors.
 
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Welcome to PF. If you check out the rules you will find that you need to do some work. First, identify the relevant equations and second, show your attempt at a solution. From there, we would have something to discuss.
 
I need your help because I do not understand how to start these exercises left me doubt if they can do would be helpful
 
Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
The value of H equals ## 10^{3}## in natural units, According to : https://en.wikipedia.org/wiki/Natural_units, ## t \sim 10^{-21} sec = 10^{21} Hz ##, and since ## \text{GeV} \sim 10^{24} \text{Hz } ##, ## GeV \sim 10^{24} \times 10^{-21} = 10^3 ## in natural units. So is this conversion correct? Also in the above formula, can I convert H to that natural units , since it’s a constant, while keeping k in Hz ?
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