Project 15: Part B: Boar Tigers - They're so hot right now

The lore built up around boar tigers may be wrong. Four intrepid scientists have a theory. It turns out that boar tigers may not be naturally aggressive, however, they become agitated in the heat. Our scientists and engineers believe that if a boar-tiger can be cooled they will become very docile. Unfortunately, they cannot cool themselves, their bodies have not properly adapted to the post-apocalyptic heat. Your job is to make a giant fan to cool off the boar-tigers. Since they are currently overheated and angry, your teams of scientists and engineers decide to set up a way to launch one block (mass 100kg) into another block (mass 200kg) from a cliff that is 500 meters tall, using a spring (with a constant of 9001 N/m). The second block must leave the cliff with a velocity of 20m/s. The second block will fall and hit the edge of the giant fan and stick to the fan as the fan has been coated with an adhesive and cause it to spin. In order to successfully cool the boar tigers, the team believes the fan must rotate between 5 and 10 radians per second. If it spins too slowly, it will not sufficiently cool the boar-tigers. If it spins too quickly, it will scare them, making them even more aggressive. The fan will be made of two blades (length 20m, mass $2\pi$ kg) salvaged from a destroyed Home Depot. You need to find out how much spring extension you need to launch the second block off the cliff with a velocity of 20m/s and whether or not the block will cause the fan to rotate quickly enough.