relativity question?

[vcestudent94]

Two rockets are each 1000 m long in their rest frame. Rocket Orion, traveling at 0.900c relative to the earth, is overtaking rocket Sirius, which is poking along at a mere 0.700c. According to the crew on Sirius, how long does Orion take to completely pass?

That is, how long is it from the instant the nose of Orion is at the tail of Sirius until the tail of Orion is at the nose of Sirius?

The way I went about it was first I calculated the velocity of Orion with respect to Sirius using the Lorentz transformation equation to get v=1.62*10^8 m/s
I then calculated the length contraction so the new length would be L=841.3m, then simply divided this length by the speed to get t=5.188 micro s.
Can someone please help identify what i did wrong? thanks

[vcestudent94]

Never mind I got it, I forgot to add the length of the other rocket so the distance should be 1841m

[jadams]

I got the same, any chance you could post your full working though? Cheers

[vcestudent94]

w = (u + v)/(1 + u*v/c^2) with w=0.9c and u=0.7c

L = (1 - v^2/c^2)*l    with l=1000 and v=from above equation

time = (L + 1000)/v