Distance from an initial position that two objects will meet

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1. Apr 26, 2016

Amelina Yoo

1. The problem statement, all variables and given/known data
40kg girl and 8.4kg sled are 15m apart on the surface of a frozen lake. By means of a rope, girl exerts a horizontal force of 5.2N on the sled, pulling it towards her.

How far from the girls initial position do they meet?
2. Relevant equations
f=ma

3. The attempt at a solution
I found that the acceleration of the sled is 0.62ms^-2 and the acceleration of the girl is 0.13ms^-2. However, I do not know where to advance at this point. I tried to find time, but to do so I need speed, and speed requires time.

Thank you if you are able to help me :-)

2. Apr 26, 2016

Simon Bridge

Instead of concentrating on what you don't know - why not write down what you do know.
You know initial positions and times and velocities for eg.
You also know some equations relating these to final positions and times ... start with those.
Keep the unknowns as variables. You may have to use algebra to solve the problem.