Answer
After throwing all the tools, the astronaut is moving with a speed of $0.30~m/s$
Work Step by Step
The initial momentum of the system is zero. By conservation of momentum, if the tools gain a certain momentum $p_t$ in one direction, the astronaut will gain the same magnitude of momentum $p_a$ in the opposite direction.
We can find the speed $v_a$ of the astronaut:
$p_a = p_t$
$m_a~v_a = m_w~v_w+m_s~v_s+m_m~v_m$
$v_a = \frac{m_w~v_w+m_s~v_s+m_m~v_m}{m_a}$
$v_a = \frac{(0.72~kg)(5.0~m/s)+(0.80~kg)(8.0~m/s)+(1.2~kg)(6.0~m/s)}{58~kg}$
$v_a = 0.30~m/s$
After throwing all the tools, the astronaut is moving with a speed of $0.30~m/s$.
