document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=99132>Question 99132</A>: <I><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 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #72171 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=72171\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation you are looking for is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+-%281%2F2%29%28a%29t%5E2+%2B+v%5Bo%5D%2At+%2B+h%5Bo%5D ALIGN=MIDDLE  ALT=\"h+=+-%281%2F2%29%28a%29t%5E2+%2B+v%5Bo%5D%2At+%2B+h%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "in which the letters represent the following:<BR>\n" );
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document.write( "h = the height above ground at the time t (in feet)<BR>\n" );
document.write( "t = the elapsed time after the object is released (in seconds)<BR>\n" );
document.write( "vo = the initial vertical velocity in feet per second that the object has at release<BR>\n" );
document.write( "ho = the initial height above ground when the object is released<BR>\n" );
document.write( "a = the acceleration in feet per second^2 due to gravity (usually 32 ft/sec^2 is acceptable)<BR>\n" );
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document.write( "The initial vertical velocity (vo) of the object is zero because the object is not thrown<BR>\n" );
document.write( "upward or downward. It is just released. Therefore, the term <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v%5Bo%5D%2At ALIGN=MIDDLE  ALT=\"v%5Bo%5D%2At\"   DISABLED_style= \"max-width:90%; height:auto;\" > is zero and<BR>\n" );
document.write( "can be deleted from the equation.<BR>\n" );
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document.write( "The initial height of the object <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 1400 feet because that is the height above<BR>\n" );
document.write( "ground of the object when it is released.<BR>\n" );
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document.write( "After an unknown number of seconds passes, the object hits the ground and at that time<BR>\n" );
document.write( "its height above ground is zero. Therefore, we can set h equal to zero.<BR>\n" );
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document.write( "With these substitutions into the equation (including that a = 32) the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-%281%2F2%29%2A%2832%29%2At%5E2+%2B+1400 ALIGN=MIDDLE  ALT=\"0+=+-%281%2F2%29%2A%2832%29%2At%5E2+%2B+1400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiply the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%281%2F2%29%2A%2832%29 ALIGN=MIDDLE  ALT=\"-%281%2F2%29%2A%2832%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get -16. Substitute this into the equation and it becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-16%2At%5E2+%2B+1400 ALIGN=MIDDLE  ALT=\"0+=+-16%2At%5E2+%2B+1400\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the 1400 on the right side by subtracting 1400 from both sides to make the <BR>\n" );
document.write( "equation become:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1400+=+-16%2At%5E2 ALIGN=MIDDLE  ALT=\"-1400+=+-16%2At%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide both sides of this equation by -16, the multiplier of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5E2 ALIGN=MIDDLE  ALT=\"t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the equation<BR>\n" );
document.write( "reduces to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1400%2F-16+=+87.5+=+t%5E2 ALIGN=MIDDLE  ALT=\"-1400%2F-16+=+87.5+=+t%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve for t by taking the square root of both sides:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2887.5%29+=+t ALIGN=MIDDLE  ALT=\"sqrt%2887.5%29+=+t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Calculator time ... the square root of 87.5 seconds^2 is 9.354143467 seconds<BR>\n" );
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document.write( "So the answer to this problem is about 9.4 seconds<BR>\n" );
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document.write( "No sense in having too much accuracy. The acceleration due to gravity on Earth is probably<BR>\n" );
document.write( "closer to 32.2 feet per second^2 and it varies depending upon where you are on the globe.<BR>\n" );
document.write( "But for most physics problems 32 feet per second^2 is close enough.<BR>\n" );
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document.write( "Hope this helps you to understand the problem.  If you get into calculus a little (1st<BR>\n" );
document.write( "semester probably) you'll find out where the equation that we used comes from.<BR>\n" );
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