Calculus

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The ideas we are practicing in these exercises can be put to practical use. A calculus teacher's son likes to shoot arrows. He was wondering at what speed the arrow leaves the bow when it is released. So they went to a large deserted beach at the Great Salt Lake and shot the bow at an angle of 45 degrees. The arrow hit the ground at a distance of 600 feet. All of this was measured very roughly, but let's work with these figures, and let's ignore air resistance. For simplicity let's also assume that the arrow is released at an initial height of 0 feet. As usual, assume that gravity causes an object to accelerate at 32 feet per second squared.
The arrow leaves the bow at what speed in miles per hour?

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