A 70 kg astronaut floating in space throws a 5 kg wrench with a speed of 10 m/s. What is the recoil speed of the astronaut?

Core Concept

In the absence of external forces, momentum is conserved. Initially, the total momentum is zero (astronaut and wrench are at rest). After throwing, the momentum of the wrench is m_wrench * v_wrench = 5 kg * 10 m/s = 50 kg·m/s. For momentum to be conserved, the astronaut must have equal and opposite momentum: m_astronaut * v_astronaut = -50 kg·m/s. Therefore, v_astronaut = -50 kg·m/s / 70 kg = -0.71 m/s. The negative sign indicates direction opposite to the wrench, so the magnitude is 0.71 m/s.