The surface of planet Xyz, in a galaxy far away is mostly an ocean of Nitric Acid. The planet is inhabited by two tribes of human-like creatures, the Blue People and the Green people, who live in separate islands. They know of each other’s existence because they had a common origin, but because of the corrosive nature of the ocean, they have not made actual contact with each other since the ocean turned acid 10 million years ago. One hundred years ago, word got out somehow, that these two peoples professed significantly different religious beliefs. The Blue people’s holy book stated that “thou shall never show your feet” (or something to that effect) and they wore concrete shoes to make sure their feet were never exposed. The green’s people Holy Scripture stated that sitting down was a mortal sin and disrespectful of God. Well, the scandal that the news ensued was of biblical proportions, as the Green people imagined all those Blue folks sitting down and offending God, while the Blue people were disgusted beyond constraint, thinking of those green and insultingly exposed toes. Both Islands managed to declare war on the other, not even knowing where the other island actually was. Pacifists from both islands were labeled ungodly and unpatriotic by political leaders and angry radio-show-hosts, and despite their best effort could not stop the nonsense. Armed with large catapults, they began throwing large rocks decorated with insults, towards the horizon and in all directions, in hopes of destroying the infidels. Their military developed larger and larger catapults, until finally, lookouts in each island began to see the incoming boulders splashing into the ocean. Now they both knew in what direction to shoot. Realizing their dilemma shots became less frequent. Scouts from both islands were sent out in boats to more precisely determine the path of incoming boulders. The scouts knew how far they were from their own shore, and they could determine and record the exact altitude of the boulders that passed over their heads. They reported the following set of data: At 20 kilometers from shore the incoming boulders were located at 2800 meters of altitude. At 40 kilometers from shore, they were spotted at 4200 meters of altitude. And at 70 kilometers out, the boulders were passing at 5550 meters of altitude. Despite their obvious limitations, Blue and Green scientists determined that the trajectories of boulders release by catapults were perfect parabolas. You are a prisoner of these mad people and to save your own skin, you are required to use the information gathered by the scouts and answer the following questions (in a way that it is clear to them): 1. How far from their shore is their enemies catapult? 2. Are their shots too short or too long to hit us and by how much? Hint: read carefully and use the tools available to you. Please, explain your work. Create a graph.
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