document.write( "Question 404845: The equation h=-16t^2+80t models the height h feet reached in t seconds by an object propelled straight up from the ground. How long will the object be in the air until it hits the ground? \n" ); document.write( "

Algebra.Com's Answer #286181 by jsmallt9(3758) $\"\"$ $\"About$

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$\"h=-16t%5E2%2B80t\"$
\n" ); document.write( "The key for this problem is recognizing that if the object is back on the ground, then its height, h, would be zero. So if we replace the h with zero, then we can solve for the time, t:
\n" ); document.write( " $\"0=-16t%5E2%2B80t\"$
\n" ); document.write( "The easiest way to solve this is by factoring. This factors quite easily:
\n" ); document.write( " $\"0=16t%28-t%2B5%29\"$
\n" ); document.write( "From the Zero Product Property we know that this (or any) product can be zero only if one (or more) of the factors is zero. So:
\n" ); document.write( "16t = 0 or -t+5 = 0
\n" ); document.write( "Solving these we get:
\n" ); document.write( "t = 0 or t = 5
\n" ); document.write( "The t=0 solution represents the fact that at the start, just before being propelled into the air, the object is on the ground. The t=5 time represents the time when the object returns to the ground. So the answer to your problem is:
\n" ); document.write( "The object will return to the ground after 5 seconds. \n" ); document.write( "

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