document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=53230>Question 53230</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 3) 	Suppose a baseball is shot up from the ground straight up with an initial velocity of 32 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0 <BR>\n" );
document.write( "•	16 represents 1/2g, the gravitational pull due to gravity (measured in feet per second2). <BR>\n" );
document.write( "•	v0 is the initial velocity (how hard do you throw the object, measured in feet per second).<BR>\n" );
document.write( "•	s0 is the initial distance above ground (in feet). If you are standing on the ground, then s0 = 0.<BR>\n" );
document.write( "a) 	What is the function that describes this problem?<BR>\n" );
document.write( "Answer: \r<BR>\n" );
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document.write( "b) 	The ball will be how high above the ground after 1 second?<BR>\n" );
document.write( "Answer:	<BR>\n" );
document.write( "Show work in this space.	\r<BR>\n" );
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document.write( "c) 	How long will it take to hit the ground?<BR>\n" );
document.write( "Answer:	<BR>\n" );
document.write( "Show work in this space. \r<BR>\n" );
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document.write( "d) 	What is the maximum height of the ball?  What time will the maximum height be attained?<BR>\n" );
document.write( "Answer:\r<BR>\n" );
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document.write( "Show work in this space.	\r<BR>\n" );
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document.write( "Thank You </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #35499 by </B><A HREF=/tutors/aboutme.mpl?userid=funmath><B>funmath(2933)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=funmath><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=35499\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you need a calculus way of solving this, let me know and I will edit this to include calculus.<BR>\n" );
document.write( "a) v0=32; s0=0; <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=-16t%5E2%2Bv0t%2Bs0 ALIGN=MIDDLE  ALT=\"s=-16t%5E2%2Bv0t%2Bs0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=-16t%5E2%2B32t%2B0 ALIGN=MIDDLE  ALT=\"s=-16t%5E2%2B32t%2B0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=-16t%5E2%2B32t ALIGN=MIDDLE  ALT=\"s=-16t%5E2%2B32t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "b)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=-16%281%29%5E2%2B32%281%29 ALIGN=MIDDLE  ALT=\"s=-16%281%29%5E2%2B32%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=-16%2B32 ALIGN=MIDDLE  ALT=\"s=-16%2B32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s=16 ft.<BR>\n" );
document.write( "----------------------------------<BR>\n" );
document.write( "c) The position s=0 when the ball hits the ground.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-16t%5E2%2B32t ALIGN=MIDDLE  ALT=\"0=-16t%5E2%2B32t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-16t%28t-2%29 ALIGN=MIDDLE  ALT=\"0=-16t%28t-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-16t=0<BR>\n" );
document.write( "-16t/-16=0/-16<BR>\n" );
document.write( "t=0s.  This is the time we threw the ball.<BR>\n" );
document.write( "t-2=0<BR>\n" );
document.write( "t-2+2=0+2<BR>\n" );
document.write( "t=2 s.  This is the time that the ball hit the ground.<BR>\n" );
document.write( "--------------------------------------------------------<BR>\n" );
document.write( "d)This is a parabolic function and it's maximum value occurs at its vertex.  There are a couple of ways to find the vertex.  If your taking caluculus, this is where you would do something different than what I'm showing you now.<BR>\n" );
document.write( "The x value of the vertex can be found by putting your function in standard form.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=at%5E2%2Bbt%2Bc ALIGN=MIDDLE  ALT=\"s=at%5E2%2Bbt%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-b%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"t=-b%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In your problem:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-16t%5E2%2B32t ALIGN=MIDDLE  ALT=\"t=-16t%5E2%2B32t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a=-16, b=32<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=-%2832%29%2F%282%2A-16%29 ALIGN=MIDDLE  ALT=\"t=-%2832%29%2F%282%2A-16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28-32%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"t=%28-32%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t=1 s.  (At 1 s. the ball is as high as it will go.)<BR>\n" );
document.write( "Substitute that into your function to find out how high it will go.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=-16%281%29%5E2%2B32%281%29 ALIGN=MIDDLE  ALT=\"s=-16%281%29%5E2%2B32%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=-16%281%29%2B32%281%29 ALIGN=MIDDLE  ALT=\"s=-16%281%29%2B32%281%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s=-16+32<BR>\n" );
document.write( "s=16 ft.  That is how high the ball will go in a perfect physics universe. </SPAN>\n" );
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