4.9 m/s to the right
Explanation:
We are going to use the conservation law of linear momentum to find her velocity. Initially, they are motionless so their initial total momentum is zero. Let's assume that anything moving to the left has a negative velocity and anything moving to the right has a positive velocity. We can write the conservation law of momentum as
[tex]0 = M_mv_m + M_wv_w[/tex]
where
[tex]M_m[/tex] = mass of the man = 55 kg
[tex]v_m[/tex] = velocity of the man = -4.3 m/s
[tex]M_m[/tex] = mass of the woman = 48 kg
[tex]v_w[/tex] = velocity of the woman
[tex]\Rightarrow 0 = (55\:\text{kg})(-4.3\:\text{m/s}) + (48\:\text{kg})v_w[/tex]
Solving for [tex]v_w,[/tex]
[tex]v_w = \left(\dfrac{55\:\text{kg}}{48\:\text{kg}}\right)(4.3\:\text{m/s}) = 4.9\:\text{m/s}[/tex]
going to the right.
