document.write( "Question 186740: When an arrow is shot in the air, the height of the arrow h(t),at time t, t>or equal to 0, is determined by the equation h(t)= -4tsquared +16t+1.For which interval of time is the height of the arrow greater than or equal to 11 meters?\r
\n" ); document.write( "\n" ); document.write( "I figured out the vertex (2,17) and roots are in decimals-.0615528128 and 4.061552813. I believe the 4.061552813 is how long it takes to go up and down, reaching 17 meters going up, but I don't know how long for 11 meters. I missed on how to do this I was sick all week and have no one to explain it to me. Please help me. Chantal Laroche \n" ); document.write( "
Algebra.Com's Answer #140031 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
When an arrow is shot in the air, the height of the arrow h(t), at time t,
\n" ); document.write( "t>or equal to 0, is determined by the equation h(t)= -4tsquared + 16t + 1.
\n" ); document.write( "For which interval of time is the height of the arrow greater than or equal to 11 meters
\n" ); document.write( ":
\n" ); document.write( "h(t) = -4t^2 + 16t + 1, where t = time in seconds, and h = height at t time.
\n" ); document.write( ":
\n" ); document.write( "There are three parts to the equation:
\n" ); document.write( "-4t^2 is the effect of gravity (usually it's 4.9t^2)
\n" ); document.write( "16t is the upward velocity of the arrow
\n" ); document.write( "1 is the height above ground (0) that the arrow is launched
\n" ); document.write( ":
\n" ); document.write( "If you plot this equation, it would look like this:
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-2%2C+5%2C+-10%2C+20%2C+-4x%5E2%2B16x%2B1%2C+11%29+\"
\n" ); document.write( "where height is on the y axis and time in sec on the x axis
\n" ); document.write( "You can see the vertex is 2,17 as you stated
\n" ); document.write( "the green line is at 11 meters
\n" ); document.write( ":
\n" ); document.write( "To calculate the time (t) that the arrow is at 11 meters; h(t) = 11
\n" ); document.write( "-4t^2 + 16t + 1 = 11
\n" ); document.write( ":
\n" ); document.write( "-4t^2 + 16t + 1 - 11 = 0
\n" ); document.write( ":
\n" ); document.write( "-4t^2 + 16t - 10 = 0
\n" ); document.write( "Use the quadratic formula: a=-4, b=16, c=-10
\n" ); document.write( "two solutions
\n" ); document.write( "t = .775 sec on the way up
\n" ); document.write( "and
\n" ); document.write( "t = 3.225 sec on the way down
\n" ); document.write( "therefore the arrow is => 11m between .775 sec to 3.225 sec or for 3.225-.775 = 2.45 sec
\n" ); document.write( ":
\n" ); document.write( "Did this help you understand what's going on here? \n" ); document.write( "
\n" );