Two spaceships are travelling in opposite directions towards each other. According to an observer on Earth, spaceship A is moving at a speed of 0.8c in the +x direction and spaceship B is moving at 0.6c in the -x direction. The observer also measures the separation of the spaceships to be 4.0x10^12m at t = 0. Both spaceships are 100m in length, according to the Earth observer.
i) Calculate the respective proper lengths of the spaceships.
ii) Calculate the relative speed of the spaceships, as observerd from one of the spaceships.
iii) Calculate the length of each spaceship as measured by the other spaceship.
iv) Calculate the time until collision according to the Earth observer.
v) Calculate the time until collision according to spaceship A.
A space traveller takes off from Earth and moves at a speed 0.988c towards the star Vega, which is 26ly away. How much time with have elapsed on the Earth clocks when:
i) The traveller reaches Vega
ii) The Earth observers recieve word from him that he has arrived
iii) How much older will the Earth observers calculate the traveller to be when he reaches Vega, than he was when he started the trip?
Observesr S and S' stand at the origins of their respective frames, which are moving relative to each other at a speed of 0.6c. Each has a standard clock, which, they set to zero when the two origins coincide. Observer S keeps the S' clock visually in sight.
i) According to the observer S, what time will the S' clock record be when the S clock records 5µs
ii) What time will observer S actually read on the S' clock when the S clock reads 5µs
