document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=111036>Question 111036</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Height in feet of a baseball above ground is given by h(t)=-16t^2+32t+3 where t represents the time in seconds after the baseball is thrown.\r<BR>\n" );
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document.write( "If you throw the ball into the air, how many seconds have passed until the ball hits the ground??\r<BR>\n" );
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document.write( "I really don't understand how to put this problem in the equations it's supposed to go into and I don't understand how to solve them...help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #81024 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=81024\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The Height in feet of a baseball above ground is given by h(t)=-16t^2+32t+3 where t represents the time in seconds after the baseball is thrown.<BR>\n" );
document.write( "If you throw the ball into the air, how many seconds have passed until the ball hits the ground?? <BR>\n" );
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document.write( "Look at the three elements of the equation:<BR>\n" );
document.write( "-16t^2 is the force of gravity, negative because it is pulling it down<BR>\n" );
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document.write( "+32t is the speed of the ball upward when it is thrown<BR>\n" );
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document.write( "+3 is the point above the ground that the ball thrown<BR>\n" );
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document.write( "t is in seconds<BR>\n" );
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document.write( "h = height in feet<BR>\n" );
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document.write( "When the ball hits the ground the height is 0,  so we have:<BR>\n" );
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document.write( "-16t^2 + 32t + 3 = 0<BR>\n" );
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document.write( "Use the quadratic formula to find t; a = -16; b = 32; c = 3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-32+%2B-+sqrt%28+32%5E2+-+4%2A+-16+%2A+3+%29%29%2F%282%2A-16%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-32+%2B-+sqrt%28+32%5E2+-+4%2A+-16+%2A+3+%29%29%2F%282%2A-16%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-32+%2B-+sqrt%281024+-+%28-192%29+%29%29%2F%28-32%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-32+%2B-+sqrt%281024+-+%28-192%29+%29%29%2F%28-32%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-32+%2B-+sqrt%281024+%2B+192+%29%29%2F%28-32%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-32+%2B-+sqrt%281024+%2B+192+%29%29%2F%28-32%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-32+%2B-+sqrt%281216+%29%29%2F%28-32%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-32+%2B-+sqrt%281216+%29%29%2F%28-32%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-32+-+34.87%29%2F%28-32%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-32+-+34.87%29%2F%28-32%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >; we only want this solution<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-66.87%29%2F%28-32%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-66.87%29%2F%28-32%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "t = +2.089 sec, when it hits the ground<BR>\n" );
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document.write( "A graph would look like this.   Vertical = height; horizontal = time in sec         <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-2%2C+4%2C+-10%2C+25%2C+-16x%5E2%2B32x%2B3%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-2%2C+4%2C+-10%2C+25%2C+-16x%5E2%2B32x%2B3%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that it crosses the y axis at 3' when t = 0 and max height is about 19 ft at 1 sec<BR>\n" );
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document.write( "Did this help you understand this? </SPAN>\n" );
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