Force that applied on the girl and on the sled must be same as there is no other external force on this system
So we can use Newton's II law to find the acceleration of them
a) Acceleration of sled
[tex]F = ma[/tex]
[tex]4.2 = 8.2*a[/tex]
[tex]a = 0.512 m/s^2[/tex]
a) Acceleration of girl
[tex]F = ma[/tex]
[tex]4.2 = 38*a[/tex]
[tex]a = 0.11 m/s^2[/tex]
C) Since there is no external force on this system so they both will meet at the position of center of mass of this system
[tex]x_{cm} = \frac{m_1x_1+m_2x_2}{m_1+m_2}[/tex]
[tex]x_{cm} = \frac{38*0 + 8.2*15}{38+8.2}[/tex]
[tex]x_{cm} = 2.66 m[/tex]
