Final answer:
According to Newton's second law, the girl's acceleration is calculated as a = F/m = 4.60 N / 31.9 kg = 0.144 m/s². This is because the force she applies on the boy is equal and opposite to the force the boy applies on her, so she also experiences a net force of 4.60 N.
Step-by-step explanation:
In order to calculate the magnitude of the girl's acceleration, we must apply Newton's second law, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (a = F/m). In this scenario, the net force applied to the boy is 4.60 N and his mass is 58.4 kg. To find the acceleration of the boy (a), we use the equation a = F/m, which gives us a = 4.60 N / 58.4 kg = 0.08 m/s².
However, the question asks for the girl's acceleration. According to Newton’s third law, the force that the girl applies on the boy through the rope is equal and opposite to the force the boy applies on the girl. Therefore, the girl also experiences a net force of 4.60 N but in the opposite direction. Given her mass is 31.9 kg, her acceleration (a) will be a = F/m = 4.60 N / 31.9 kg = 0.144 m/s² in the direction towards the boy.
Learn more about Newton's Laws of Motion