Final answer:
Using the work-energy principle, the work done by the wind on the child on the swing is calculated to be 226.98 joules, as all of this work went into increasing the child's kinetic energy to 3.89 m/s at the bottom of the swing.
Step-by-step explanation:
To determine how much work was done by the wind on the child on the swing, we can use the work-energy principle. This principle states that the work done on an object is equal to the change in its kinetic energy. In this scenario, we start by calculating the kinetic energy at the bottom of the swing before the wind acts on the child.
The initial kinetic energy (KEinitial) at the maximum angle (when the child momentarily stops) is 0 J since the velocity is 0 m/s. We can then calculate the final kinetic energy (KEfinal) when the child reaches the bottom with a speed of 3.89 m/s using the formula KE = 0.5 * m * v2, where m is the mass of the child, and v is the velocity.
Plug in the values:
KEfinal = 0.5 * 30.0 kg * (3.89 m/s)2
KEfinal = 0.5 * 30.0 kg * 15.1321 m2/s2
KEfinal = 226.98 J
Since the initial kinetic energy was 0 J, the work done by the wind is equal to the final kinetic energy:
Work by the wind = KEfinal - KEinitial
Work by the wind = 226.98 J - 0 J
Work by the wind = 226.98 J
Therefore, the wind did 226.98 joules of work on the child.