Free Fall

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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 = -16t2 + 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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Answer

h = -16t2 + 144

we want to know when h = 0, so simply
substitute 0 for h and solve for t...

0 = -16t2 + 144    << add 16t2 to both sides >>

16t2 = 144           << divide both sides by 16 >>

   t2 =  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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