document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=162782>Question 162782</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618503080/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> A mode rocket is launched with an initial velocity of 200ft/s. The height (h), in feet, of the rocket (t) seconds after the launch is given by <BR>\n" );
document.write( "h = -16t^2 +200t. How many seconds after the launch will the rocket be 300 ft above the ground? Round to the nearest hundredth of a second.\r<BR>\n" );
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document.write( "So far I have it set up as such but no sure if its correct.\r<BR>\n" );
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document.write( "200t-300= -16t^2 + 200t - 200t\r<BR>\n" );
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document.write( "help appreciated.<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 #120004 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=120004\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> initial velocity = 200 feet / second.<BR>\n" );
document.write( "h = height of the rocket in feet.<BR>\n" );
document.write( "t = number of seconds after launch.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "h = -16t^2 + 200t<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "the question is: in how many seconds will the rocket be 300 feet above the ground.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since h = -16t^2 + 200t, then if we want h to be 300 feet above the ground, the equation becomes<BR>\n" );
document.write( "300 = -16t^2 + 200t<BR>\n" );
document.write( "subtracting 300 from both sides of the equation and it becomes<BR>\n" );
document.write( "-16t^2 + 200t - 300 = 0<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "can't really see which factors would work by looking at the equation, so i will use the quadratic formula.<BR>\n" );
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document.write( "for the quadratic formula<BR>\n" );
document.write( "a = -16<BR>\n" );
document.write( "b = 200<BR>\n" );
document.write( "c = -300<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "b = 200<BR>\n" );
document.write( "b^2 = 40000<BR>\n" );
document.write( "4ac = -16 * 4 * -300 = 19200<BR>\n" );
document.write( "2a = -32<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b+%2B+sqrt+%28b%5E2-4%2Aa%2Ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"%28-b+%2B+sqrt+%28b%5E2-4%2Aa%2Ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-200+%2B+sqrt+%2840000-19200%29%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"%28-200+%2B+sqrt+%2840000-19200%29%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "t = 1.733060906 seconds.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-b+-+sqrt+%28b%5E2-4%2Aa%2Ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"%28-b+-+sqrt+%28b%5E2-4%2Aa%2Ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > becomes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-200+-+sqrt+%2840000-19200%29%29%2F%28-32%29 ALIGN=MIDDLE  ALT=\"%28-200+-+sqrt+%2840000-19200%29%29%2F%28-32%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which becomes<BR>\n" );
document.write( "t = 10.75693909<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "t can be either 1.73.... or 10.75693.....<BR>\n" );
document.write( "substituting in the original equation shows the following<BR>\n" );
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document.write( "using t = 1.733060906:<BR>\n" );
document.write( "300 = -16 * t^2 + 200t becomes<BR>\n" );
document.write( "300 = -16*(1.733060906)^2 + 200 * (1.733060906)<BR>\n" );
document.write( "this becomes 300 = 300<BR>\n" );
document.write( "looks like 17.3... is a good solution.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "using t = 10.75693909<BR>\n" );
document.write( "300 = -16 * (10.75693909)^2 + 200 * (10.75693909)<BR>\n" );
document.write( "this becomes 300 = 300<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "it looks like t could be either<BR>\n" );
document.write( "1.733060906<BR>\n" );
document.write( "or<BR>\n" );
document.write( "10.75693909<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since the initial velocity is 200 feet / second, we can calculate how far the rocket traveled in either of those seconds assuming that velocity is stable until the rocket has at least reached 300 feet.<BR>\n" );
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document.write( "taking 1.733..., the rocket will have traveled 200 feet per second * 1.733... seconds = 346.6 feet<BR>\n" );
document.write( "in order for it to reach 300 feet it would have to have been aimed almost straight up.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "taking 10.756..., the rocket will have traveled 200 feet per second * 10.756... seconds = 2151 feet.<BR>\n" );
document.write( "this allows a much more shallow trajectory for it to reach 300 feet.<BR>\n" );
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document.write( "both answers are plausible depending on the trajectory of the rocket and the velocity being at least as fast as when it was initially launched.<BR>\n" );
document.write( "answers are:<BR>\n" );
document.write( "t can be either...<BR>\n" );
document.write( "1.733060906<BR>\n" );
document.write( "or<BR>\n" );
document.write( "10.75693909<BR>\n" );
document.write( "-----<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );