Project 12: Part A: Engineering a movie stunt

Once our stunt person who is playing Ethan is on top of the building an attack drone flies down to attack him. It turns out he had another spindle wheel of exactly the same dimensions and mass attached to him as the first wheel (m = 0.5 kg, the outer radius of 6.2cm and an inner radius of 2cm) and the drone has latched onto this and started pulling with a force equivalent to the force of gravity that was applied to Ethan as he fell from the building. This force is being applied directly horizontally to Ethan so that the drone is trying to pull him off the top of the building. Meanwhile, Ethan is still attached to the wire that helped him get to the top of this new building. Ethan is 25 meters from the edge of the building. How far does the drone have to travel so that Ethan will be at the edge of the building and what speed will Ethan be traveling at when he gets there?

Some initial testing of spindle wheels of different masses and radii have shown (for a constant force) that the relationship between the angular speed of the reel and the linear speed of Ethan is related to the ratio of the masses of the Ethan and reel. The equation that best fits this data is given below,

$$\omega_{\rm wheel} = \dfrac{M_{\rm ethan}}{m_{\rm wheel}}\dfrac{v_{\rm ethan}}{R_{\rm wheel}}$$