In order to estimate the height of a bridge over water, you throw a small stone horizontally over the approximately level river below. If it takes 2 seconds before you see the splash, estimate the height of the bridge. Use $10 \mathrm{~m} / \mathrm{s}^{2}$ for the magnitude of the acceleration due to gravity and for best results, don't use a calculator!
$30 \mathrm{~m}$
$40 \mathrm{~m}$
$10 \mathrm{~m}$
$20 \mathrm{~m}$
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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 = \(\boxed{20}\) \(\mathrm{m}\).