document.write( "Question 202853: If a juggler can toss a ball into the air with a velocity of 64ft/sec from a height of 6 ft, then what is the maximum height reached by the ball? \n" ); document.write( "
Algebra.Com's Answer #153021 by Earlsdon(6294)\"\" \"About 
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The height (h) of an object propelled upwards as a function of time (t) is given by:
\n" ); document.write( "\"h%28t%29+=+-%281%2F2%29gt%5E2%2Bv%5B0%5Dt%2Bh%5B0%5D\" where g, the constant of acceleration due to gravity is 32ft/sec^2, \"v%5B0%5D\" is the initial upwards velocity, and \"h%5B0%5D\" is the initial height of the object.
\n" ); document.write( "In this problem, \"v%5B0%5D+=+64\"ft/sec. and \"h%5B0%5D+=+6\"ft.
\n" ); document.write( "Making the appropriate substitutions into the function above, we get:
\n" ); document.write( "\"h%28t%29+=+-16t%5E2%2B64t%2B6\"
\n" ); document.write( "This equation, when graphed, is a parabola that opens downwards, so we are looking for the maximum point (the vertex) on the curve which will give us the maximum height attained by the juggler's ball.
\n" ); document.write( "The value of the independent variable (t in this case) at the vertex is given by:
\n" ); document.write( "\"t+=+%28-b%29%2F2a\" where b = 64 and a = -16.
\n" ); document.write( "\"t+=+%28-64%29%2F2%28-16%29\"
\n" ); document.write( "\"t+=+2\"seconds. This is the time, t, at which the juggler's ball reaches its maximum height. To find the actual maximum height, we substitute t = 2 into the function above and solve for h.
\n" ); document.write( "\"h%282%29+=+-16%282%29%5E2%2B64%282%29%2B6\" Evaluate.
\n" ); document.write( "\"h%282%29+=+-16%284%29%2B128%2B6\"
\n" ); document.write( "\"h%282%29+=+-64%2B128%2B6\"
\n" ); document.write( "\"h%282%29+=+70\"
\n" ); document.write( "The maximum height reached by the ball is 70 feet.
\n" ); document.write( "\"graph%28400%2C400%2C-5%2C5%2C-5%2C74%2C-16x%5E2%2B64x%2B6%29\"
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