document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=275603>Question 275603</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Throwing a wrench. An angry construction worker throws<BR>\n" );
document.write( "his wrench downward from a height of 128 feet with an<BR>\n" );
document.write( "initial velocity of 32 feet per second. The height of the<BR>\n" );
document.write( "wrench above the ground after t seconds is given<BR>\n" );
document.write( "by S(t)= -16t^2  32t + 128.<BR>\n" );
document.write( "a) What is the height of the wrench after 1 second?<BR>\n" );
document.write( "b) How long does it take for the wrench to reach the<BR>\n" );
document.write( "ground? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #201000 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=201000\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "Your height function is improperly stated.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ S(t)\ =\ \frac{1}{2}gt^2\ +\ v_ot\ +\ s_o\">\r<BR>\n" );
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document.write( "Where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large g\"> is the acceleration in feet per second due to gravity, namely <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -32\text{ \frac{ft}{sec^2}\">\r<BR>\n" );
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document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large v_o\"> is the initial velocity, here <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -32\text{ \frac{ft}{sec}\">\r<BR>\n" );
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document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large s_o\"> is the initial height, here 128 feet.\r<BR>\n" );
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document.write( "Hence:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ S(t)\ =\ -16t^2\ +\ (-32)t\ +\ 128\">\r<BR>\n" );
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document.write( "The height of the wrench after 1 second is the value of the function when <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large t\ =\ 1\">.  Plug in the value and do the arithmetic:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ S(1)\ =\ -16(1)^2\ +\ (-32)(1)\ +\ 128\">\r<BR>\n" );
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document.write( "The height of the ground is zero, so the time value when <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large S(t)\ =\ 0\"> is the length of time it takes for the wrench to hit the ground -- presuming that the wrench didn't hit something else, perhaps the worker's boss' head -- before it hit the ground.  So, solve the quadratic:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ -16t^2\ +\ (-32)t\ +\ 128\ =\ 0\">\r<BR>\n" );
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document.write( "Hint: First factor out -16\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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