Question

An astronaut is repairing a portion of the space station. In doing so, he threw a 5.25-kg monkey wrench away from him at 1.20 m/s to the right. If he has a mass of 72 kg, with what speed and in what direction will he begin to move

Answer 1

Apply momentum conservation. The initial momentum is 0 (the astronaut and wrench are motionless), then the momentum is

$$0=m_av_a+m_wv_w,\\\space\\ v_a=v_w\frac{m_w}{m_a}=1.2\frac{2.25}{72}=0.0375\text{ m/s}.$$