= Solution
The capsule continues inertially at $v_c/c=350/353$ while the ship reduces its station-frame <speed> to $0.7c$. Transform the ship's new <velocity> into the capsule frame:
$$
\boxed{\frac{v_{s/c}}c=\frac{0.7-350/353}{1-0.7(350/353)}=-\frac{343}{360}\simeq-0.952778.}
$$
Thus its <speed> is $0.952778c$, and the negative sign means it recedes behind the capsule along the chosen axis. The same transformation compares the subsequent local inertial <velocities>; the details of the intervening deceleration are not needed.
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