Step 1 :Let h(t) represent the height of the stone at time t. The equation for the height of the stone is given by h(t) = -\(\frac{1}{2}\)gt^2 + h_0, where g is the acceleration due to gravity and h_0 is the initial height.
Step 2 :We are given that g = 10 \(\mathrm{m/s^2}\) and t = 2 seconds.
Step 3 :Substitute the given values into the equation: h(2) = -\(\frac{1}{2}\)(10)(2)^2 + h_0.
Step 4 :Simplify the equation: h(2) = -20 + h_0.
Step 5 :Since h(2) represents the height of the stone when it hits the water, we know that h(2) = 0.
Step 6 :Substitute h(2) = 0 into the equation: 0 = -20 + h_0.
Step 7 :Solve for h_0: h_0 = \(\boxed{20}\) \(\mathrm{m}\).