A person walking across a bridge 144 feet above the water decides to drop a rock and watch the splash. The model formula for the height h of the rock at time t is: h = 16t^{2} + 144 where t is measured in seconds and 144 is the original height (in feet) of the rock above the water. How long does it take for the rock to hit the water? [answer]


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h = 16t^{2} + 144 we want to know when h
= 0, so simply 0 = 16t^{2} + 144 << add 16t^{2} to both sides >> 16t^{2} = 144 << divide both sides by 16 >> t^{2} = 9 << take the square root of both sides >> t^{ } = ± 3 Since "negative seconds" doesn't make sense, the answer is t = 3, or it takes 3 seconds for the rock to hit the water. N.B. In a case like this, t = 3 is called an extraneous solution 
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