The recoil speed of the archer is 0.20 m/s
Work Step by Step
Since the initial momentum of the system (archer and arrow) is zero, the magnitude of the archer's final momentum $p_a$ should be equal to the magnitude of the arrow's final momentum $p_w$. We can equate the magnitudes of the momenta to find the recoil speed $v$ of the archer. $p_a = p_w$ $(50~kg)~v = (0.10~kg)(100~m/s)$ $v = 0.20~m/s$ The recoil speed of the archer is 0.20 m/s.