Step 1 :The water will hit the surface of the pond when the height of the jet of water is zero, i.e., when \(y=0\). So, we need to solve the equation \(-2x^2 + 8x + 1 = 0\) for \(x\).
Step 2 :This is a quadratic equation, and we can solve it using the quadratic formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\), where \(a = -2\), \(b = 8\), and \(c = 1\).
Step 3 :However, since the distance cannot be negative, we only consider the positive root.
Step 4 :By substituting the values of \(a\), \(b\), and \(c\) into the quadratic formula, we get two roots \(x1 = 4.121320343559642\) and \(x2 = -0.12132034355964239\).
Step 5 :Since the distance cannot be negative, we discard \(x2\) and take \(x1\) as the distance from the nozzle to where the water hits the surface of the pond.
Step 6 :Rounding to the nearest hundredth, we get \(x = 4.12\) feet.
Step 7 :Final Answer: The water will hit the surface of the pond approximately \(\boxed{4.12}\) feet from the nozzle.