document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=77919>Question 77919</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I really need help with the following problem.  Thank you!\r<BR>\n" );
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document.write( "Science and Medicine:  Find the time required for an object to fall to the ground from a building that is 1400 ft. high.  Show thew formula and solve.\r<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 #55839 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=55839\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the time required for an object to fall to the ground from a building that is 1400 ft. high.<BR>\n" );
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document.write( "The equation for the height of a falling body is (assuming you neglect air resistance <BR>\n" );
document.write( "which would slow the rate of fall a little and therefore increase the time that it takes):<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+%28g%2F2%29%2At%5E2+%2B+%28V%5Bo%5D%2At%29+%2B+h%5Bo%5D ALIGN=MIDDLE  ALT=\"h%28t%29+=+%28g%2F2%29%2At%5E2+%2B+%28V%5Bo%5D%2At%29+%2B+h%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "in which the terms are defined as follows:<BR>\n" );
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document.write( "h(t) = height as it relates to the time t<BR>\n" );
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document.write( "g = acceleration due to gravity. Usually we use a value of -32 ft/sec^2 for g, but it <BR>\n" );
document.write( "really depends where you are on the globe. If you are on top of Mount Everest, the value<BR>\n" );
document.write( "of gravity is different from if you are way down in Death Valley, California. It's not<BR>\n" );
document.write( "a big difference, but it is different. (The minus sign on gravity is just to show that<BR>\n" );
document.write( "it acts downward toward the center of the Earth.)<BR>\n" );
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document.write( "t = time elapsed in seconds<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bo%5D ALIGN=MIDDLE  ALT=\"V%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the initial velocity. If you throw the object up or if you throw the object <BR>\n" );
document.write( "down, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bo%5D ALIGN=MIDDLE  ALT=\"V%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > will have a value. If you just let go of the object, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bo%5D ALIGN=MIDDLE  ALT=\"V%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > will be zero. In<BR>\n" );
document.write( "this problem the object is just released so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bo%5D=0 ALIGN=MIDDLE  ALT=\"V%5Bo%5D=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5Bo%5D ALIGN=MIDDLE  ALT=\"h%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the initial height of the object at t = 0 seconds. In this case the initial <BR>\n" );
document.write( "height is 1400 ft because the object is 1400 feet above ground at the time of release.<BR>\n" );
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document.write( "Substituting -32 for g, zero for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bo%5D ALIGN=MIDDLE  ALT=\"V%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and 1400 for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5Bo%5D ALIGN=MIDDLE  ALT=\"h%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > changes the general<BR>\n" );
document.write( "equation to one applicable to this problem.  With these substitutions the equation <BR>\n" );
document.write( "becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+-16t%5E2+%2B+1400 ALIGN=MIDDLE  ALT=\"h%28t%29+=+-16t%5E2+%2B+1400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice that when t = 0, the equation reduces to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29+=+1400 ALIGN=MIDDLE  ALT=\"h%28t%29+=+1400\"   DISABLED_style= \"max-width:90%; height:auto;\" > which tells you that at<BR>\n" );
document.write( "the instant of release the object is at 1400 ft above the ground.<BR>\n" );
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document.write( "How high will the object be when it hits ground?  The height above ground at the time of<BR>\n" );
document.write( "impact will be zero. Substitute 0 for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28t%29 ALIGN=MIDDLE  ALT=\"h%28t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the equation to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-16t%5E2+%2B+1400 ALIGN=MIDDLE  ALT=\"0+=+-16t%5E2+%2B+1400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "You can eliminate the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-16t%5E2 ALIGN=MIDDLE  ALT=\"-16t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the right side by adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16t%5E2 ALIGN=MIDDLE  ALT=\"16t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides<BR>\n" );
document.write( "to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16t%5E2+=+1400 ALIGN=MIDDLE  ALT=\"16t%5E2+=+1400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide both sides by 16 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2+=+1400%2F16+=+87.5 ALIGN=MIDDLE  ALT=\"t%5E2+=+1400%2F16+=+87.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and solve for t by taking the square root of both sides to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+sqrt%2887.5%29+=+9.354 ALIGN=MIDDLE  ALT=\"t+=+sqrt%2887.5%29+=+9.354\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So the answer is that it takes the object about 9.354 seconds after release to fall 1400 ft.<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better. </SPAN>\n" );
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