**re: HSC Physics Marathon Archive**
This ones' from my trials: The distance to Alpha Centauri is 4.367 light years as measured from earth. using relevant calculation explain how a rocket could complete the journey from earth to alpha centauri in exactly 3.28 years.

Try not to use trial and error; my teachers still gave full marks to those who solved it with trial and error, but it takes the fun out of it

Due to the effect of length contraction, the journey will appear less than 4.367 light years for those within the spacecraft, which means that they may be able to journey in 3.28 years. Quantitatively,

d = 4.367*c(1-v^2/v^2)^0.5

t = d/v

Using these equations, with t = 3.28 and the contracted length, we get that:

v^2 = (4.37*c)^2/(4.37^2 + 3.28^2)

v = 2.399x10^8 m/s

Hence, if the spacecraft were to be travelling at 2.399x10^8 m/s, it would be able to travel to alpha centauri in exactly 3.28 years