Answer:
-1.67 m/s
Explanation:
We can solve this problem by using the law of conservation of momentum: in fact, since the system is isolated (no external forces, since the ice is frictionless), the total momentum of Evelyin and Lily must be conserved.
The total momentum before is zero, since they are both at rest:
[tex]p_i = 0[/tex]
The total momentum after is:
[tex]p_f = mv+MV[/tex]
where
m = 48.3 kg is Lily's mass
M = 57.4 kg is Evelyin's mass
V = 1.4 m/s is Evelyn's velocity
v is the Lily's velocity
Since momentum is conserved,
[tex]p_i=p_f[/tex]
And so
[tex]0=mv+MV[/tex]
Solving for v, we find Lily's velocity:
[tex]v=-\frac{MV}{m}=-\frac{(57.4)(1.4)}{48.3}=-1.67 m/s[/tex]
And the negative sign indicates that her direction is opposite to Evelyn's direction.
