Force on rope and acceleration

[72beeflee]

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...

 

[Delphi51]

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.

 

[kerimek]

I would like to clarify that the given problem does not provide enough information to accurately calculate the distance from the girl's initial position where they meet. While the acceleration of the girl and sled can be calculated using the given force and masses, the time it takes for them to meet and the initial velocities are not given. Without this information, it is not possible to accurately calculate the distance.

Additionally, the given problem assumes a frictionless surface, which is not realistic. In reality, there will always be some amount of friction present, which will affect the acceleration and distance traveled.

To provide a more accurate solution, we would need to know the initial positions and velocities of both the girl and sled, as well as the coefficient of friction between the sled and the ice. Only then can we accurately calculate the distance they will meet.

In terms of the equation F=ma, it is important to note that this equation only applies to objects with constant acceleration. In this problem, the acceleration of the girl and sled will not be constant due to the changing forces (5.0 N) and the presence of friction. Therefore, we cannot use this equation to solve the problem.

In conclusion, the given problem does not provide enough information to accurately calculate the distance where the girl and sled will meet. Further information, such as initial positions and velocities, and the coefficient of friction, is needed to provide a more accurate solution.