A 31.9 kg boy and a 55.6 kg girl are on the surface of a frozen lake, 10.0 m apart. Using a rope, the boy exerts a horizontal 5.05 N force on the girl, pulling her toward him. Calculate the magnitude of the boy's acceleration.
Acceleration can be calculated using Newton's Second Law:
Based on the situation above, we can also use Newton's Third Law to say that the force acting on the girl is the same as the force acting on the boy.
Knowing the boy's mass and the force acting on the boy, it is a simple matter to calculate his acceleration using the formula above.
Assumptions: The frozen lake surface can be considered to be frictionless.
Notes: In a problem like this it is important to recognize when you have more information than necessary. The length of the rope and the mass of the girl are not needed in this calculation.