Final answer:
To balance the seesaw, the person on the other end must have a mass of 17.4 kg, as calculated by setting the product of their mass, gravitational acceleration, and distance from the fulcrum equal to the moment created by the 29-kg child on the opposite side.
Step-by-step explanation:
To balance the seesaw, the moments (torques) on both sides of the fulcrum must be equal. The moment on one side is the product of the force (weight of the child) and the distance from the fulcrum. The seesaw is in static equilibrium, which means the net torque around the fulcrum must be zero.
The 29-kg child creates a moment of 29 kg × 9.8 m/s² × 1.5 m, as the distance from the fulcrum to where the child is sitting is 4.0 m - 2.5 m = 1.5 m. To balance this, the person on the other end must create an equal moment. Therefore, the mass of the person m times the acceleration due to gravity 9.8 m/s² and the distance from the fulcrum 2.5 m must be equal to the moment created by the child.
Setting up the equation: m × 9.8 m/s² × 2.5 m = 29 kg × 9.8 m/s² × 1.5 m. Solving for m, we find that m = (29 kg × 1.5 m) / 2.5 m = 17.4 kg.
The person on the other end must have a mass of 17.4 kg to balance the seesaw.