document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=977919>Question 977919</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When a stone is projectad into the air with a vertical speed  of 25m/s,its height in meters above the ground after t seconds is given by h=26+5t^<BR>\n" );
document.write( "Draw the graph of h=26t-5t^ for values  of t from 0 to 6 taking  2cm to represent 10units of h. From your graph estimate <BR>\n" );
document.write( "1)After how many seconds the stone will hit the ground<BR>\n" );
document.write( "the ground <BR>\n" );
document.write( "2)the greatest height <BR>\n" );
document.write( "3)for how many seconds is the stone more than 30 meters above the ground <BR>\n" );
document.write( "4)find the speed of the stone  at 3seconds </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #599429 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=599429\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When a stone is projected into the air with a vertical speed  of 25m/s, its height in meters above the ground after t seconds is given by h=26+5t^<BR>\n" );
document.write( "Draw the graph of h=26t-5t^ for values  of t from 0 to 6 taking  2cm to represent 10units of h. From your graph estimate<BR>\n" );
document.write( "h=26+5t^   ************** This is wrong.  It's -5t^2, not plus.<BR>\n" );
document.write( "h=26t-5t^  ************* This would be correct if you add the exponent 2.<BR>\n" );
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document.write( "You say 25 m/sec, but the equations say 26 ???<BR>\n" );
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document.write( "Using 25 m/sec for the launch:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-5t%5E2+%2B+25t ALIGN=MIDDLE  ALT=\"h%28t%29+=+-5t%5E2+%2B+25t\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (notice the exponent 2)\r<BR>\n" );
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document.write( " <BR>\n" );
document.write( "1)After how many seconds the stone will hit the ground<BR>\n" );
document.write( "the ground <BR>\n" );
document.write( "It impacts at h(t) = 0<BR>\n" );
document.write( "-5t^2 + 25t = 0<BR>\n" );
document.write( "Solve for t.<BR>\n" );
document.write( "(t = 0 is the launch)<BR>\n" );
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document.write( "2)the greatest height <BR>\n" );
document.write( "Max height is the vertex of the parabola, at t = -b/2a<BR>\n" );
document.write( "t = -25/-10 = 2.5 seconds after launch<BR>\n" );
document.write( "max ht = h(2.5)<BR>\n" );
document.write( "3)for how many seconds is the stone more than 30 meters above the ground<BR>\n" );
document.write( "-5t^2 + 25t = 30<BR>\n" );
document.write( "Solve for t.<BR>\n" );
document.write( "height > 30 is the difference between the 2 times, going up, then descending.<BR>\n" );
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document.write( "4)find the speed of the stone at 3 seconds<BR>\n" );
document.write( "Launch speed = 25 m/sec<BR>\n" );
document.write( "Using h(t) = -5t^2 + 25t, acceleration = -10m/sec/sec<BR>\n" );
document.write( "25 + 3*(-10) = -5 m/sec (falling at 5 m/sec) </SPAN>\n" );
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