document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137460>Question 1137460</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What will be the time (in seconds) taken by a small stone to reach the surface of the Earth if it is dropped from a height R/4 where R = 6 400 km, Mass of Earth =6 x 10^24 kg. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #755396 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=755396\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The small stone is at rest when it is dropped from a height of 6400/4 = 1600 km<BR>\n" );
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document.write( "Note The acceleration of gravity will be less for the stone at height 1600 km than if the stone is near the surface of the earth<BR>\n" );
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document.write( "We know that<BR>\n" );
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document.write( "F = ma = GmM/r^2, where M is the mass of the earth, G is the gravitational constant, m is the mass of the stone, M is the mass of the Earth and r is distance from the center of the earth to the stone<BR>\n" );
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document.write( "The distance from the center of the earth to its surface is 6400 km, therefore r is 6400 + 1600 = 8000 km<BR>\n" );
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document.write( "a =  ( 6.677 x 10^-11 m^3 kg^-1 s^-2) * (5.972 x 10^24 kg) / (8000000)^2<BR>\n" );
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document.write( "a =   (39.875 x 10^13) / (6.4 x 10^13) = 6.23 m/sec^2<BR>\n" );
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document.write( "distance = v(0)t +(1/2)at^2, where v(0) = 0, distance = 8000000 m<BR>\n" );
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document.write( "Here, problems arise, notably the acceleration of gravity will increase as the object approaches the surface of the earth, air friction will increase as well<BR>\n" );
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document.write( "What assumptions has your teacher given you about this problem?<BR>\n" );
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