document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1102751>Question 1102751</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The height, s, of a ball thrown straight down with initial speed 32 ft/sec from a cliff 128 feet high is s(t) = –16t2 – 32t + 128, where t is the time elapsed that the ball is in the air. What is the instantaneous velocity of the ball when it hits the ground?\r<BR>\n" );
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document.write( "A) -96 ft/sec<BR>\n" );
document.write( "B) 256 ft/sec<BR>\n" );
document.write( "C) 0 ft/sec<BR>\n" );
document.write( "D) 112 ft/sec </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #717493 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=717493\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Instantaneous velocity is defined as ds/dt, or the first derivative of the distance formula<BR>\n" );
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document.write( "we want to find t when s(t) = 0<BR>\n" );
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document.write( "0 = –16t2 – 32t + 128<BR>\n" );
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document.write( "divide both sides of = by -16<BR>\n" );
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document.write( "t^2 +2t -8 = 0<BR>\n" );
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document.write( "factor the polynomial<BR>\n" );
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document.write( "(t+4) * (t-2) = 0<BR>\n" );
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document.write( "t = -4 or 2<BR>\n" );
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document.write( "we reject the negative value for t<BR>\n" );
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document.write( "ds/dt = -32t -32<BR>\n" );
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document.write( "now substitute t=2 in ds/dt<BR>\n" );
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document.write( "ds/dt = -32(2) -32 = -96<BR>\n" );
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document.write( "instantaneous velocity of the ball when it hits the ground is -96 ft/sec<BR>\n" );
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document.write( "Answer is A)<BR>\n" );
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