document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=277866>Question 277866</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. (20 points) In 1981, Vadimir Poliakov (USSR) set a world record of 19ft ¾ in for the pole vault (www.polevault.com).  To reach that height, Poliakov obtained a speed of approximately 36 feet per second on the runway.  The formula h = -16t2 + 36t gives his height t seconds after leaving the ground.	<BR>\n" );
document.write( "a.	Does the graph of this equation open up or down? How did you determine this? <BR>\n" );
document.write( "b.	Describe what happens to his height as time passes, starting at t=0? <BR>\n" );
document.write( "c.	Use the method of your choice to find how long he was in the air.<BR>\n" );
document.write( "d.	Will his height peak or be at a low during the middle of the time he is in the air? How do you know? <BR>\n" );
document.write( "e.	After how many seconds will the peak or low occur? <BR>\n" );
document.write( "f.	How high will he be when the peak or low occurs? <BR>\n" );
document.write( "g.	What is the point of the vertex? How does this number relate to your answers in parts e and f? <BR>\n" );
document.write( "h.	How many solutions are there to the equation 0 = -16t2 + 36t? How do you know? <BR>\n" );
document.write( "i.	To use the quadratic formula to solve an equation like this, we need three values, represented in your text by a, b and c.  In the equation in part h, what are a, b & c?<BR>\n" );
document.write( "j.	What do the solutions to 0 = -16t2 + 36t  represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense? <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #202269 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=202269\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In 1981, Vadimir Poliakov (USSR) set a world record of 19ft ¾ in for the pole vault (www.polevault.com). To reach that height, Poliakov obtained a speed of approximately 36 feet per second on the runway. The formula h = -16t^2 + 36t gives his height t seconds after leaving the ground. <BR>\n" );
document.write( "a. Does the graph of this equation open up or down? How did you determine this?<BR>\n" );
document.write( "Ans: Down because of the -16t^2<BR>\n" );
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document.write( "b. Describe what happens to his height as time passes, starting at t=0?<BR>\n" );
document.write( "Ans: h(0) = 0 means the height is zero when the time is zero.<BR>\n" );
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document.write( "c. Use the method of your choice to find how long he was in the air.<BR>\n" );
document.write( "Ans: Solve h=0 for two values of \"t\".<BR>\n" );
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document.write( "d. Will his height peak or be at a low during the middle of the time he is in the air? How do you know?<BR>\n" );
document.write( "Ans: peak because the parabola opens down and therefore has a peak at the vertex.<BR>\n" );
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document.write( "e. After how many seconds will the peak or low occur?<BR>\n" );
document.write( "Ans: Find the t-value of the peak at t = -b/2a<BR>\n" );
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document.write( "f. How high will he be when the peak or low occurs?<BR>\n" );
document.write( "Ans: Find h at that t-value.<BR>\n" );
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document.write( "g. What is the point of the vertex? How does this number relate to your answers in parts e and f?<BR>\n" );
document.write( "Ans: vertex has time of peak and height of peak.<BR>\n" );
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document.write( "h. How many solutions are there to the equation 0 = -16t2 + 36t? How do you know?<BR>\n" );
document.write( "Ans: It is a quadratic<BR>\n" );
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document.write( "i. To use the quadratic formula to solve an equation like this, we need three values, represented in your text by a, b and c. In the equation in part h, what are a, b & c?<BR>\n" );
document.write( "Ans a = -16 ; b = 36 ; c = 0<BR>\n" );
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document.write( "j. What do the solutions to 0 = -16t2 + 36t represent? Is there a solution that does not make sense? If so, in what ways does the solution not make sense?<BR>\n" );
document.write( "Ans: They both tell the time when the vaulter is on the ground.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.  <BR>\n" );
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