Tug-of-War Forces: Solving the Rope Problem

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In a tug-of-war scenario involving a 69-kg boy and a 48-kg girl on a frictionless surface, the girl accelerates toward the boy at 3.0 m/s². The discussion highlights the application of Newton's laws of motion to analyze the forces involved. Initially, there was confusion about how to approach the problem and create a free-body diagram. After seeking assistance, the individual was able to understand the concepts and successfully solve the problem. The interaction emphasizes the importance of understanding fundamental physics principles in solving dynamics problems.
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Homework Statement


Suppose a 69-kg boy and a 48-kg girl use a massless rope in a tug-of-war on an icy, resistance-free surface. If the acceleration of the girl toward the boy is 3.0 m/s2, find the magnitude of the acceleration of the boy toward the girl.

Homework Equations


f=ma
fg=mg
fnet=mAnet
Ff=μῦF

The Attempt at a Solution


I don't understand how to solve it. Or draw a free-body diagram...and go from there.
 
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Apply Newton's third law.
 
I don't understand how that would help me to solve the problem. Can you help me get started please?
 
Nevermind, I was asking too much for a simple problem. I understand it now and I solved it. Thank you for your help!
 

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Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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