document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=283298>Question 283298</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hi, my question is following<BR>\n" );
document.write( "A toy rocket is launched straight up from the top of a building 50 ft tall at an initial velocity of 200 ft per sec. Using the function V(x)=-16t^2+vt+h, answer the following.<BR>\n" );
document.write( "1. Give the function that describes the height of the rocket in terms of t?<BR>\n" );
document.write( "2. Determine the time at which the rocket reaches its maximum height, and its maximum height in feet?<BR>\n" );
document.write( "3. For what time interval will the rocket be more than 300 ft above the ground level?<BR>\n" );
document.write( "4. for how many seconds will it hit the ground? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #205718 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=205718\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = t.\r<BR>\n" );
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document.write( "your equation becomes V(x) = -16x^2 + vt + h\r<BR>\n" );
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document.write( "h = 50 which is the height of the rocket at time point 0 (value of x is 0).\r<BR>\n" );
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document.write( "your equation becomes v(x) = -16x^2 + vx + 50\r<BR>\n" );
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document.write( "Since initial velocity is 200 ft/sec, then v = 200 and your equation becomes:\r<BR>\n" );
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document.write( "v(x) = -16x^2 + 200x + 50\r<BR>\n" );
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document.write( "maximum height should be when x = -b/2a\r<BR>\n" );
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document.write( "a = -16<BR>\n" );
document.write( "b = 200<BR>\n" );
document.write( "c = 50\r<BR>\n" );
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document.write( "maximum height should be when x = -200/-32 = 6.25\r<BR>\n" );
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document.write( "when x = 6.25, v(x) = 675 feet.\r<BR>\n" );
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document.write( "That's what the maximum height should be.\r<BR>\n" );
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document.write( "Set v(x) = 300 and solve for x.\r<BR>\n" );
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document.write( "300 = -16x^2 + 200x + 50\r<BR>\n" );
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document.write( "subtract 50 from both sides of this equation to get 0 = -16x^2 + 200x - 250.\r<BR>\n" );
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document.write( "solve for the roots of this equation by quadratic formula.\r<BR>\n" );
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document.write( "a = -16<BR>\n" );
document.write( "b = 200<BR>\n" );
document.write( "c = -250\r<BR>\n" );
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document.write( "(-b +/- sqrt(b^2 - 4ac))/(2a) =:<BR>\n" );
document.write( "(-200 +/- sqrt(200^2 - 4*-16*-200))/(-32) =:<BR>\n" );
document.write( "(-200 +/- sqrt(40000 - 12800))/(-32) =:<BR>\n" );
document.write( "(-200 +/- sqrt(27200)))=32 =:<BR>\n" );
document.write( "(-200 +/- 164.924225)/(-32)\r<BR>\n" );
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document.write( "x = 1.096117968 or x = 11.40388203\r<BR>\n" );
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document.write( "The rocket should be at or above 300 feet from x = 1.096117968 to x = 11.40388203\r<BR>\n" );
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document.write( "A graph of this equation is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C600%2C-5%2C15%2C-100%2C1000%2C-16x%5E2+%2B+200x+%2B+50%2C300%2C675%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C600%2C-5%2C15%2C-100%2C1000%2C-16x%5E2+%2B+200x+%2B+50%2C300%2C675%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A horizontal line was placed at y = 300 and 675 to show you the intersection points with the graph of the equation of the rocket.\r<BR>\n" );
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document.write( "At y = 675, the graph should be at the maximum point.\r<BR>\n" );
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document.write( "At 300, the graph should be at x = 1.09 and x = 11.4 roughly.\r<BR>\n" );
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document.write( "Trace a vertical line down from those intersection points to see the x-value.\r<BR>\n" );
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document.write( "x-value represents time in seconds.<BR>\n" );
document.write( "y-value represents height in feet.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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