document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=959507>Question 959507</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that a ball is projected upward from the top of the Mart Hotel in Dallas, Texas, which is 400 feet high. Its position s in feet above the ground is given by the equation &#119904;=&#8722;16&#119905;2+45&#119905;+400. where t is the number of seconds elapsed. \r<BR>\n" );
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document.write( "a. How long will it take for the ball to reach a height of 200 feet above the ground?\r<BR>\n" );
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document.write( "b. When will the ball hit the ground? State the answer in number of seconds after the ball was projected.\r<BR>\n" );
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document.write( "c. What is the highest point that the ball reaches before falling back to earth? At what time will it reach that point? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #586487 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=586487\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose that a ball is projected upward from the top of the Mart Hotel in Dallas, Texas, which is 400 feet high. Its position s in feet above the ground is given by the equation &#119904;=&#8722;16&#119905;2+45&#119905;+400. where t is the number of seconds elapsed. <BR>\n" );
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document.write( "a. How long will it take for the ball to reach a height of 200 feet above the ground? <BR>\n" );
document.write( "&#119904;=&#8722;16&#119905;2+45&#119905;+400<BR>\n" );
document.write( "200=&#8722;16&#119905;2+45&#119905;+400<BR>\n" );
document.write( "&#8722;16&#119905;2+45&#119905;+200=0<BR>\n" );
document.write( "solve for t with quadratic formula: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a=-16, b=45, c=200<BR>\n" );
document.write( "ans:<BR>\n" );
document.write( "t=-2.4 s (reject)<BR>\n" );
document.write( "or <BR>\n" );
document.write( "t=5.2 s<BR>\n" );
document.write( "How long will it take for the ball to reach a height of 200 feet above the ground? 5.2 sec<BR>\n" );
document.write( "..<BR>\n" );
document.write( "b. When will the ball hit the ground? State the answer in number of seconds after the ball was projected.<BR>\n" );
document.write( "Ball will hit the ground when height=0<BR>\n" );
document.write( " &#8722;16&#119905;2+45&#119905;+400=0<BR>\n" );
document.write( "Use quadratic formula to solve:<BR>\n" );
document.write( "a=-16, b=45, c=400<BR>\n" );
document.write( "ans: t=6.6 sec<BR>\n" );
document.write( "When will the ball hit the ground? 6.6 sec<BR>\n" );
document.write( "..<BR>\n" );
document.write( "c. What is the highest point that the ball reaches before falling back to earth? At what time will it reach that point?<BR>\n" );
document.write( "&#119904;=&#8722;16&#119905;2+45&#119905;+400<BR>\n" );
document.write( "complete the square:<BR>\n" );
document.write( "s=-16(t^2-45/16+2025/1024)+2025/64+25600/64<BR>\n" );
document.write( "s=-16(t-45/32)^2+2025/64+25600/64<BR>\n" );
document.write( "s=-16(t-45/32)^2+29650/64<BR>\n" );
document.write( "s=-16(t-45/32)^2+431.64<BR>\n" );
document.write( "The ball reaches the highest point of 431.64 ft after (45/32)=1.4 sec  </SPAN>\n" );
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