document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=254720>Question 254720</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A soccer ball is kicked into the air and its height in meters above ground, h, recorded after t seconds. The height of the ball is described by the function h(t)= -3t^2+24t+1.<BR>\n" );
document.write( "a) Determine when the ball reached its maximum height. (I think 1 sec)<BR>\n" );
document.write( "b) Determine the ball's maximum height.<BR>\n" );
document.write( "c) Determine the instantanneous velocity of the projectile at t= 2.8 sec.<BR>\n" );
document.write( "d) Determine the instantaneous velocity of the projectile at t= 4.5 sec.What does the negative sign mean? ( That is is falling back to the ground?)<BR>\n" );
document.write( "e) Determine the instantaneous velocity of the projectile at t=4 sec. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #187068 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=187068\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A soccer ball is kicked into the air and its height in meters above ground, h, recorded after t seconds. The height of the ball is described by the function h(t)= -3t^2+24t+1.<BR>\n" );
document.write( "a) Determine when the ball reached its maximum height. (I think 1 sec)<BR>\n" );
document.write( "Max height is at the vertex of the parabola.<BR>\n" );
document.write( "at t = -b/2a<BR>\n" );
document.write( "t = -24/-6 = 4 seconds<BR>\n" );
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document.write( "b) Determine the ball's maximum height.<BR>\n" );
document.write( "h(4) = -3*16 + 96 + 1<BR>\n" );
document.write( "h(4) = 49 meters<BR>\n" );
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document.write( "c) Determine the instantaneous velocity of the projectile at t= 2.8 sec.<BR>\n" );
document.write( "h'(t) = -6t + 24<BR>\n" );
document.write( "h'(2.8) = -16.8 + 24<BR>\n" );
document.write( "h'(2.8) = 7.2 meters/sec (positive, going up)<BR>\n" );
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document.write( "d) Determine the instantaneous velocity of the projectile at t= 4.5 sec.What does the negative sign mean? ( That is is falling back to the ground?)<BR>\n" );
document.write( "h'(4.5) = -6*4.5 + 24<BR>\n" );
document.write( "h'(4.5) = -3 meters/second (negative --> going back down)<BR>\n" );
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document.write( "e) Determine the instantaneous velocity of the projectile at t=4 sec.<BR>\n" );
document.write( "h'(4) = -6*4 + 24 = 0 (it stops going up, and starts back down)<BR>\n" );
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document.write( "h' is the 1st derivative of height with respect to time.  I don't know how to do this without derivatives.<BR>\n" );
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