document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1092505>Question 1092505</A>: <I><SPAN STYLE=\"word-break: break-all;\"> an object in launched upward at 110 feet per second from a platform 75 feet high . \r<BR>\n" );
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document.write( "a) When will the object be 120 feet high?\r<BR>\n" );
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document.write( "b) What is its maximum height?\r<BR>\n" );
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document.write( "c) When will it 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 #707132 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=707132\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the height of the object at time t is modeled by the following formula<BR>\n" );
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document.write( "s(t) = –gt^2 + v0t + h0, where g is the acceleration due to gravity, v0 is the objects initial velocity, h0 is the initial height of the object<BR>\n" );
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document.write( "since we are working in feet, g=16, also v0=110 and h0=75<BR>\n" );
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document.write( "s(t) = -16t^2 +110t +75<BR>\n" );
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document.write( "this is a parabola that curves downward<BR>\n" );
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document.write( "the graph of this equation is <BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-2%2C+9%2C+-100%2C+300%2C+-16x%5E2%2B110x%2B75%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-2%2C+9%2C+-100%2C+300%2C+-16x%5E2%2B110x%2B75%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "a)  120 = -16t^2 +110t +75<BR>\n" );
document.write( "-16t^2 +110t -45 = 0<BR>\n" );
document.write( "t^2 -6.875t +2.8125 = 0<BR>\n" );
document.write( "use quadratic formula to solve for t<BR>\n" );
document.write( "t = (-(-6.875) +square root((-6.875)^2 -4(1)(2.8125))) / 2(1) = 6.4382 seconds<BR>\n" );
document.write( "t = (-(-6.875) -square root((-6.875)^2 -4(1)(2.8125))) / 2(1) = 0.4368 seconds<BR>\n" );
document.write( "Note that the object attains the height of 120 feet at two different times(on the way up and again on the way down)<BR>\n" );
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document.write( "b)  t = -b/2a(this is the t value associated with the vertex)<BR>\n" );
document.write( "s(t) = -16t^2 +110t +75<BR>\n" );
document.write( "t = -110 / 2(-16) = 3.4375<BR>\n" );
document.write( "s(3.4375) = -16(3.4375)^2 +110(3.4375) +75 = 264.0625 feet at its maximum height<BR>\n" );
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document.write( "c)  s is 0 when the object hits the ground<BR>\n" );
document.write( "0 = -16t^2 +110t +75<BR>\n" );
document.write( "t^2 -6.875t -4.6875 = 0<BR>\n" );
document.write( "t = (-(-6.875) +square root((-6.875)^2 -4(1)(-4.6875))) / 2(1) = 7.5<BR>\n" );
document.write( "t = (-(-6.875) +square root((-6.875)^2 -4(1)(-4.6875))) / 2(1) = -0.625<BR>\n" );
document.write( "we reject the negative value for t, therefore the object hits the ground after 7.5 seconds<BR>\n" );
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