document.write( "Question 825404: Alex throws a ball straight up into the air. The equation s = s(t) = –16t2 + 80t + 44 gives the distance s (in feet) the ball is above the ground t seconds after he throws it.\r
\n" ); document.write( "\n" ); document.write( "a) How high is the ball two seconds after he throws it?
\n" ); document.write( "b) What is the maximum height of the ball from the ground?
\n" ); document.write( "c) At what time does the ball hit the ground? \n" ); document.write( "

Algebra.Com's Answer #497260 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+s%28t%29+=+-16t%5E2+%2B+80t+%2B+44+\"$
\n" ); document.write( "(a)
\n" ); document.write( " $\"+s%28t%29+=+-16t%5E2+%2B+80t+%2B+44+\"$
\n" ); document.write( " $\"+s%282%29+=+-64+%2B+160+%2B+44%0D%0A%7B%7B%7B+s%282%29+=+140+\"$
\n" ); document.write( "In 2 sec, the ball is 140 ft high
\n" ); document.write( "--------------------------
\n" ); document.write( "(b)
\n" ); document.write( "The time , $\"t\"$ when the
\n" ); document.write( "height is maximum is
\n" ); document.write( " $\"+-b%2F%282a%29+\"$ where
\n" ); document.write( " $\"+a+=+-165+\"$
\n" ); document.write( " $\"+b+=+80+\"$
\n" ); document.write( " $\"+-b%2F%282a%29+=+-80+%2F+%282%2A%28-16%29%29+\"$
\n" ); document.write( " $\"+-b%2F%282a%29+=+80%2F32+\"$
\n" ); document.write( " $\"+-b%2F%282a%29+=+5%2F2+\"$
\n" ); document.write( "Plug this value back into equation to find $\"+s%282.5%29+\"$
\n" ); document.write( " $\"+s%282.5%29+=+-16%2A%282.5%29%5E2+%2B+80%2A2.5+%2B+44+\"$
\n" ); document.write( " $\"+s%282.5%29+=+-100+%2B+200+%2B+44+\"$
\n" ); document.write( " $\"+s%282.5%29+=+144+\"$
\n" ); document.write( "The maximum height is 144 ft
\n" ); document.write( "--------------------------
\n" ); document.write( "(c)
\n" ); document.write( "The ball hits the ground when $\"+s%28t%29+\"$ is zero for
\n" ); document.write( "the 2nd time. Find the roots of the equation
\n" ); document.write( " $\"+s%28t%29+=+-16t%5E2+%2B+80t+%2B+44+\"$
\n" ); document.write( " $\"+s%28t%29+=+0+\"$
\n" ); document.write( " $\"+-16t%5E2+%2B+80t+%2B+44+=+0+\"$
\n" ); document.write( " $\"+-4t%5E2+%2B+20t+%2B+11+=+0+\"$
\n" ); document.write( " $\"+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+\"$
\n" ); document.write( " $\"+a+=+-4+\"$
\n" ); document.write( " $\"+b+=+20+\"$
\n" ); document.write( " $\"+c+=+11+\"$
\n" ); document.write( " $\"+t+=+%28+-20+%2B-+sqrt%28+20%5E2+-+4%2A%28-4%29%2A11+%29%29+%2F+%282%2A%28-4%29%29+\"$
\n" ); document.write( " $\"+t+=+%28+-20+%2B-+sqrt%28+400+%2B+176+%29%29+%2F+%28-8%29+\"$
\n" ); document.write( " $\"+t+=+%28+-20+%2B-+sqrt%28+576+%29%29+%2F+%28-8%29+\"$
\n" ); document.write( " $\"+t+=+%28+-20+-+24%29+%2F+%28-8%29+\"$ ( I can't use the positive square root )
\n" ); document.write( " $\"+t+=+11%2F2+\"$
\n" ); document.write( "The ball hits the ground in 5.5 sec
\n" ); document.write( "Here's the plot:
\n" ); document.write( " $\"+graph%28+400%2C+400%2C+-1%2C+6%2C+-10%2C+160%2C+-16x%5E2+%2B+80x+%2B+44+%29+\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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