Force and distance traveled (sled on frozen lake)

[soccerball3211]

A 36 kg girl and a 5.3 kg sled are on the frictionless ice of a frozen lake, 11 m apart but connected by a rope of negligible mass. The girl exerts a horizontal 5.4 N force on the rope. What are the acceleration magnitudes of (a) the sled and (b) the girl? (c) How far from the girl's initial position do they meet?

For parts a and b I used the equation F=ma and solved for a

For part a I got 1.0m/s^2 and for part b I got .15m/s^2

Can someone help get me started on part C?

Thank you for the help

 

[skeeter]

let the girl be at position x = 0 at t = 0
sled is at x = 11 at t = 0

position of the girl as a function of time ...
x = (1/2)(.15)t²

position of the sled as a function of time ...
x = 11 - (1/2)(5.3/5.4)t²

set the two positions equal, solve for t, then substitute that value of t into either equation above to find the meeting position relative to the girl's initial position (x = 0)

 

[soccerball3211]

Thanks Skeeter

I got 1.4 meters approximately