ANSWER
B. 0.15 m/s
EXPLANATION
If we consider the system astronaut-hammer as an islotated system and we apply the law of conservation of momentum we have:
[tex]p=0=m_hv_h+m_Av_A[/tex]Where mh is the mass of the hammer, mA is the mass of the astronaut, vh is the hammer's final velocity and vA is the astronaut's final velocity.
In this system the velocities will be constant, because there are no other forces acting and the initial velocity for both objects is zero (because they are at rest).
Let's solve the equation above for vA:
[tex]v_A=\frac{-m_hv_h}{m_A}[/tex]The astronaut's velocity is:
[tex]v_A=\frac{-4kg\cdot3.5m/s}{91\operatorname{kg}}\approx-0.15m/s[/tex]The minus sign indicates that the astronaut is moving in the opposite direction of the hammer's motion. Therefore the correct answer is option B. 0.15m/s
