An injured monkey sits perched on a tree branch 9.0 m above the ground, while a wildlife veterinarian is kneeling down in the bushes 81.5 m away attempting to subdue the monkey with a tranquilizer gun. The vet knows that the moment the gun fires the monkey will be frightened and fall down from the branch. What angle up from the ground must the hunter aim the gun so that the tranquilizer dart will hit the falling monkey?
Given the angle above, what is minimum speed the tranquilizer dart must leave the gun to still hit the monkey?