document.write( "Question 631950: A toy rocket is launched upward from ground level with an initial velocity of 39 meters per second. Its height is a function of time, given by h = -4.9t^2+39t, where h represents the height in meters and t represents the time in seconds. What is the maximum height reached by the rocket and how long is it in flight? \n" ); document.write( "

Algebra.Com's Answer #397934 by lwsshak3(11628) $\"\"$ $\"About$

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A toy rocket is launched upward from ground level with an initial velocity of 39 meters per second. Its height is a function of time, given by h = -4.9t^2+39t, where h represents the height in meters and t represents the time in seconds. What is the maximum height reached by the rocket and how long is it in flight?
\n" ); document.write( "**
\n" ); document.write( "h = -4.9t^2+39t
\n" ); document.write( "complete the square:
\n" ); document.write( "h=-4.9(t^2-(39/4.9)t)
\n" ); document.write( "39/4.9≈7.96
\n" ); document.write( "(1/2*7.96)^2=3.98^2=15.84) (half the coefficient of t)^2
\n" ); document.write( "h=-4.9(t^2-7.96t+15.84)+77.62
\n" ); document.write( "h=-4.9(t-3.98)^2+77.62
\n" ); document.write( "This is an equation of a parabola that opens downwards so it has a maximum at the vertex.
\n" ); document.write( "Its standard form: y=(x-h)^2+k, (h,k)=(x,y) coordinates of the vertex.
\n" ); document.write( "For given problem:
\n" ); document.write( "Vertex: (3.98,77.62)
\n" ); document.write( "maximum height: 77.62 meters
\n" ); document.write( "flight time: 3.98 seconds \n" ); document.write( "

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