document.write( "Question 214441: a ball is kicked into the air and follows the path described by
\n" ); document.write( "h(t)-4.9t^2+6t+0.6. where t is the time in seconds and h is the height in meters abouve the ground. Detrmine the maximum height of the ball to the nearest tenth of a meter. \n" ); document.write( "

Algebra.Com's Answer #161990 by Earlsdon(6294) $\"\"$ $\"About$

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Find the maximum height:
\n" ); document.write( " $\"h%28t%29+=+-4.9t%5E2%2B6t%2B0.6\"$
\n" ); document.write( "First find the time t, at which the ball reaches its maximum height.
\n" ); document.write( "This can be found by noting that the curve described by this quadratic equation (this is necessarily the trajectory of the ball) is a parabola that open downward. The maxumum point on this parabola occurs at the vertex of the parabola.
\n" ); document.write( "The x-coordinate (t-coordinate in this problem) is found by:
\n" ); document.write( " $\"t+=+-b%2F2a\"$ where, from the given equation, a = -4.9 and b = 6.
\n" ); document.write( " $\"t+=+-6%2F2%28-4.9%29\"$
\n" ); document.write( " $\"t+=+0.6122\"$ seconds. Now substitute this value of t into the given equation and solve for $\"h%5Bm%5D\"$ , the maximum height.
\n" ); document.write( " $\"h%5Bm%5D%280.6122%29+=+-4.9%280.6122%29%5E2%2B6%280.6122%29%2B0.6\"$
\n" ); document.write( " $\"h%5Bm%5D%280.6122%29+=+2.43\"$ meters.
\n" ); document.write( "The maximum height of the ball is 2.4 meters.
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