In frame S, two balls are travelling along the x axis directly to each other, both have the same speed c/2. They are 150x10^8m apart. being that c=3x10^8ms^-1
a) in frameS, how long does it take to reach each other?
b) given the answer to a), at what speed is the distance between the
c) one objects is at the rest frmae, how long does it take the objects to reach each other if thery are 150x10^8m apart?
d)Now in frame S the two objects are again going towards each other, but now with different speed (v,u). They start "d" away from each other?
In the same frame, how long do they take to reach each other?
The way I solved this problem was
a) v=d/t, therefore t=d/v, so i plugged in (150x10^8/2)/(c/2)
b) I'm struggling. In this case i wrote down c, because is asking the whole distance so i just added both speeds (c/2+c/2). Am i right? can someone explain in details
c)since it's a frame in rest and the other moving I used t'=γ(t-(v/c^2)x) and i plugged in the numbers since i know t,distace(150x10^8) and v(c/2).
d) I'm lost. I know that if my b is correct the speed is going to decrease by that amount but then how should I approach this problem?