00:01
We start with the information we're given, noting that the distance is relative to the earth star reference frame, and the time that we're given in years is relative to the ship reference frame.
00:14
The time given is related to the earth star's time by the formula you see here.
00:21
So delta t prime divided by the square root of 1 minus v squared over c squared gives us the time that will elapse relative to someone on the earth.
00:31
So if we go ahead and proceed, we can go ahead and write an expression for the velocity as delta x divided by delta t.
00:40
But using the lorentz transformation for the time that we have written, we can also write the velocity as delta x over delta t prime times the square root of one minus v squared over c squared.
00:53
And we're going to use this second form actually to get the velocity that we want.
00:58
And so when we do this, we go ahead and write it out.
01:01
And we square both sides and first we're going to establish a formula and then we'll insert the numbers that we're given so we know delta x and delta t prime will insert those numbers and this will finally give us a value for the velocity so we go ahead and in squaring we move all terms in v squared to one side of the equation and notice that the right hand side will equal one so now what we do is we factor out v squared over c squared.
01:40
In doing that, we now will have delta t prime over delta x squared times c squared plus 1 in brackets, multiplying v squared over c squared...