Answer
$124.9\space m/s$
Work Step by Step
Please see the attached image first.
Here we use the principle of conservation of momentum, $\vec P= constant$
We can write, $m_{1}\vec u_{1}= m_{2}\vec V_{2}+m_{3}\vec V_{3}$
Let's choose x - axis along the horizontal direction, y - axis along the vertical direction. Then the two components of the momentum conservation equation become,
x component : $m_{SC}V_{x}=m_{o}V_{ox}+m_{L}V_{Lx}-(1)$
y component : $m_{SC}V_{y}=m_{o}V_{oy}+m_{L}V_{Ly}-(2)$
Let's plug known values into these equations.
$(1)=\gt$
$1176\space kg\times V_{x}=784\space kg\times 225\space m/s\space +392\space kg\times(-75.4\space m/s)$
$V_{x}= 124.9\space m/s$
$(2)=\gt$
$1176\space kg\times V_{y}=784\space kg\times 107\space m/s\space +392\space kg\times(-214\space m/s)$
$V_{y}=0$
The velocity of the composite spacecraft $= 124.9\space m/s$
