# Problem 4 – Hint 4

As the fourth hint, let us write a few starting lines of the solution.
The 4-velocity $u$ of the frame (A) has the components $(1,0,0)$ in frame (A), the components $(\gamma c, -\gamma V, 0)$ in frame (B), and the components $(\gamma' c, -\gamma' P, \gamma' Q)$ in frame (C). Here $V$ denotes the speed of the spaceship after the first stage of acceleration (which we want to determine), $P$ and $Q$ are the unknown components of the velocity of the laboratory frame in the frame (C), $\gamma=1/\sqrt{1-V^2/c^2}$, and $\gamma'=1/\sqrt{1-(P^2+Q^2)/c^2}$. Next, the 4-velocity $v$ of the frame (B) in frames (A), (B), and (C) is written as $(\gamma c, \gamma V, 0)$, $(1,0,0)$, and $(\gamma c, 0, -\gamma V)$, respectively. It should now be clear how to proceed, and use the instructions in Hint 3.

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