document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=180814>Question 180814</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Throwing a wrench. An angry construction worker throws 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 wrench above the ground after t seconds is given by S(t)= -16t^2 -32t + 128.\r<BR>\n" );
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document.write( "a) what is the height of the wrench after 1 second?\r<BR>\n" );
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document.write( "b) how long does it take for the wrench to reach the ground?<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 #135552 by </B><A HREF=/tutors/aboutme.mpl?userid=eperette><B>eperette(173)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=eperette><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=135552\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> S(t)= -16t^2 -32t + 128\r<BR>\n" );
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document.write( "(a) need to find S(t) when t=1\r<BR>\n" );
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document.write( "S(1)= -16(1)^2 - 32(1) + 128<BR>\n" );
document.write( "S(1)= -16 -32 + 128<BR>\n" );
document.write( "S(1)= 80\r<BR>\n" );
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document.write( "At t=1second the height of the wrench is 80ft\r<BR>\n" );
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document.write( "(b)if the wrench reaches the ground, then the height is 0, ...in other words it is asking you to find t when S(t)=0....you can solve this problem two ways\r<BR>\n" );
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document.write( "(Graphing Method) <BR>\n" );
document.write( "With your calculator, graph the equation...your solution will be your zeros (or x-intercepts)....notice that x-intercepts happen at t=-4 and t=2....t=-4 does not make sense so your answer should be t=2 seconds\r<BR>\n" );
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document.write( "(Algebra Method)\r<BR>\n" );
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document.write( "0 = -16t^2 - 32t +128<BR>\n" );
document.write( "0 = t^2 -32t -2048<BR>\n" );
document.write( "0 = (t-64)(t+32)<BR>\n" );
document.write( "0 = (t-64/-16)(t + 32/-16)<BR>\n" );
document.write( "0 = (t + 4)(t-2)<BR>\n" );
document.write( "(t+4)=0 or (t-2)=0<BR>\n" );
document.write( "t=-4 or t=2<BR>\n" );
document.write( "it would not make sense of the time to be negative....so this leaves us with one answer:  the wrench reaches the ground when t=2 seconds </SPAN>\n" );
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