A fountain has jets that squirt water in all directions at a speed of 16 ft/sec from a central point as shown. The dotted curve shows the boundary between the "dry" region (which the fountain doesn't reach) and the "wet" region reached by the water spray. Find the shape of this dotted curve, giving an equation for it (y as a function of x). Ignore any air resistance, and assume that g is exactly 32 ft/sec2.
Hint: Given the starting angle θ of a drop of water, write down y and x as a function of t, and eliminate t to get y as a function of x. Use some trigonometric identities to rewrite this equation so that it only involves tanθ and not the sine or cosine. Now suppose that you are at some point (x,y) in space. Show how to find the starting angle θ such that the water will reach that point. You will have a quadratic equation for tanθ which sometimes has real solutions (meaning the water will get to you) and sometimes has no real solutions (meaning the water won't get to you). Find the condition for the borderline case.
