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A rocket is scheduled to lift off from a stage 2ft. off the ground at an initial velocity of 80ft. per sec. How long is the rocket in the air? Use 32 ft/sec as the acceleration rate of gravity(G). What will be the maximum height of the rocket? The converted formula for the height of an object propelled unto the air is h=-16t squared +vt+h sub zero
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\n" ); document.write( "They give you the equation as:
\n" ); document.write( "h(t) = -16t squared + vt + \"h sub zero\"
\n" ); document.write( "where
\n" ); document.write( "h(t) is height
\n" ); document.write( "t is time
\n" ); document.write( "v is velocity
\n" ); document.write( "\"h sub zero\" is initial height
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\n" ); document.write( "Given the data from the problem we now have:
\n" ); document.write( "h(t) = -16t^2 + 80t + 2
\n" ); document.write( "This is a parabola.
\n" ); document.write( "It opens downward (from the coefficient associated with the t^2 term).
\n" ); document.write( "So, finding the axis of symmetry gives you the peak.
\n" ); document.write( "\"axis of symmetry\" = -b/2a = -80/(2*(-16)) = -80/-32 = 2.5
\n" ); document.write( "So, when
\n" ); document.write( "t = 2.5 seconds
\n" ); document.write( "it will be at its peak.
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\n" ); document.write( "To find the height, plug t back into:
\n" ); document.write( "h(t) = -16t^2 + 80t + 2
\n" ); document.write( "h(2.5) = -16(2.5)^2 + 80(2.5) + 2
\n" ); document.write( "h(2.5) = 102 feet\r
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