Force on rope and acceleration

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A 32 kg girl and an 8.4 kg sled are connected by a rope on frictionless ice, with the girl exerting a horizontal force of 5.0 N. The girl's acceleration is calculated to be 0.156 m/s², while the sled's acceleration is 0.595 m/s². To determine how far they meet from the girl's initial position, the total acceleration towards each other is considered. Using the equation for constant acceleration, the time to meet is calculated, followed by determining the distance the girl travels in that time. This approach effectively combines both perspectives to solve the problem.
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1. A 32 kg girl and an 8.4 kg sled are on the frictionless ice of a frozen lake, 16 m apart bu connected by a rope of negligible mass. The girl exerts a horozontal 5.0 force on the rope. How far from the girl's initial position do they meet?

2. Fnet=ma

3. The Attempt at a Solution :
Acceleration of girl = F/m = 5/32 = .156 m/s^2.
Acceleration of sled = F/m = 5/8.4 = .595 m/s^2.
I've been trying to use constant acceleration equations but I feel like I don't have enough information...
 
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Welcome to PF, bee.
For a moment look at it from the point of view of the girl. The sleigh appears to be accelerating toward her at .156 + .595. Use d = Vi*t + ½at² to find the time it takes to cover the distance. Once you have the time to meeting, go back to the outside point of view and work with just the girl's motion for that time.
 

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