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,

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

Your team has been hired to oversee the hanging of a new marquee outside the historic Alamo Drafthouse cinema in Austin, TX. The design calls for the marquee (mass, $200\,{\rm kg}$) to hang from the middle of a steel pole (length, $2.5\,{\rm m}$; mass, $1000\,{\rm kg}$). The pole has one end bolted to the outside of the building and is positioned horizontally. There is a hook from which your team may connect a steel cable (diameter, $1\,{\rm cm}$) to the pole for additional support; hanging the marquee to the pole alone will damage the exterior of the historic building. A hook exists at a height $1\,{\rm m}$ from where the pole would connect to the building. Your team needs to determine if the steel cable you were shipped (stress-strain data shown below) can be used to support this marquee (and where precisely you can hook the cable to the pole). The Greater Austin Historical Society will only allow you to use the existing mount on the exterior of the building. You should also check that the reaction force perpendicular to the wall due to the steel pole doesn't exceed $30,000\,{\rm N}$ because if it does it will punch through the exterior of the building.