Final answer:
The problem is a physics question involving energy conservation and work, where the final speed of a girl sliding down a slide is calculated using her initial potential energy, the work done against a drag force, and the resulting kinetic energy at the bottom.
Step-by-step explanation:
The question involves solving a problem using the principles of energy conservation and work. We need to determine Rachel's speed at the bottom of the slide while considering the effects of a drag force, suggesting an application of the work-energy principle. The slide is conceptualized as frictionless except for the described drag force. We start by equating the initial potential energy to the sum of kinetic energy and the work done against drag at the bottom.
The initial gravitational potential energy (PE) at height h is given by PE = mg, where m is Rachel's mass, g is the acceleration due to gravity (9.8 m/s2), and h is the height. When Rachel reaches the bottom, her potential energy has been converted to kinetic energy (KE) and work done against drag. The kinetic energy is given by KE = 0.5mv2, where v is her speed at the bottom. The work done by the drag force (Wdrag) is Wdrag = force × distance = Fdragd, where Fdrag is the drag force and d is the distance traveled.
By energy conservation, initial PE = KE + Wdrag, thus mgh = 0.5mv2 + Fdragd. From this, we can solve for v, the final speed.
Plugging in the values we have: (48.2 kg)(9.8 m/s2)(9.10 m) = 0.5(48.2 kg)v2 + (15.0 N)(18.2 m). Solving for v, we can ignore mass as it cancels out, and we are left to apply basic algebraic manipulations to find Rachel's final speed.