Answer
The recoil speed of the submarine is $1.0~cm/s$
Work Step by Step
We can assume the initial momentum of the system is zero. By conservation of momentum, if the torpedo gains a certain momentum $p_t$ in one direction, the submarine will gain the same magnitude of momentum $p_s$ in the opposite direction.
We can find the recoil speed $v_r$ of the submarine:
$p_s = p_t$
$m_s~v_r = m_t~v_t$
$v_r = \frac{m_t~v_t}{m_s}$
$v_r = \frac{(250~kg)(100.0~m/s)}{2.5\times 10^6~kg}$
$v_r = 0.010~m/s = 1.0~cm/s$
The recoil speed of the submarine is $1.0~cm/s$.
