document.write( "Question 205029This question is from textbook Elementary and intermediate algebra
\n" ); document.write( ": A red and green ball are tossed in the air at the same time. The red ball is given the velocity of 96 feet per second and its height (t) seconds after it is tossed is -16t^2+96t feet. The green ball is given a velocity of 80t feet per second and its height (t) seconds after it is tossed is -16t^2+80t feet. What is the polynomial difference (t) that represent the difference in the heights of the two balls? How much higher is the read ball 2 seconds after the balls are tossed? In reality, when does the difference in the heights stop increasing? Do I subtract the second polynomial term from the first to get the difference? \n" ); document.write( "
Algebra.Com's Answer #154761 by ankor@dixie-net.com(22740)\"\" \"About 
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A red and green ball are tossed in the air at the same time. The red ball is
\n" ); document.write( " given the velocity of 96 feet per second and its height (t) seconds after it
\n" ); document.write( " is tossed is -16t^2+96t feet. The green ball is given a velocity of 80t feet
\n" ); document.write( " per second and its height (t) seconds after it is tossed is -16t^2+80t feet.
\n" ); document.write( " What is the polynomial difference (t) that represent the difference in the
\n" ); document.write( "heights of the two balls? How much higher is the read ball 2 seconds after the
\n" ); document.write( " balls are tossed? In reality, when does the difference in the heights stop
\n" ); document.write( " increasing?
\n" ); document.write( " Do I subtract the second polynomial term from the first to get the difference?
\n" ); document.write( ":
\n" ); document.write( "Yes, indeed, that's what you do:
\n" ); document.write( "f(t) = (-16t^2 + 96t) - (-16t^2 + 80t)
\n" ); document.write( "Remove bracket, change signs after the negative;
\n" ); document.write( "f(t) = -16t^2 + 96t + 16t^2 - 80t
\n" ); document.write( ":
\n" ); document.write( "f(t) = -16t^2 + 16t^2 + 96t - 80t
\n" ); document.write( ":
\n" ); document.write( "f(t) = 16t; the difference between the height of the two balls
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\n" ); document.write( "How much higher is the red ball 2 seconds after the balls are tossed?
\n" ); document.write( "t = 2
\n" ); document.write( "f(t) = 16(2)
\n" ); document.write( "f(t) = 32 ft higher is the red ball
\n" ); document.write( ":
\n" ); document.write( " In reality, when does the difference in the heights stop increasing?
\n" ); document.write( ":
\n" ); document.write( "When the green ball hits the ground height, h = 0
\n" ); document.write( "Find the time when the height of the green ball = 0
\n" ); document.write( "-16t^2 + 80t = 0
\n" ); document.write( "Factor out -16t
\n" ); document.write( "-16t(t - 5) = 0
\n" ); document.write( "the solution we want is
\n" ); document.write( "t = 5 seconds
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "A graph will illustrate this nicely
\n" ); document.write( ":
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-4%2C+8%2C+-20%2C+150%2C+-16x%5E2%2B96x%2C+-16x%5E2%2B80x%29+\"
\n" ); document.write( "Note the green ball strikes the ground after 5 sec, while the red ball is still in the air, After 6 sec, both are on the ground and the difference is 0 \n" ); document.write( "
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