document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=153914>Question 153914</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The formula: R (sub a) = R (sub f)sqrt{1-(v/c)^2}\r<BR>\n" );
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document.write( "expresses the aging rate of an astronaut. R (sub a), relative to the aging rate of a friend on Earth, R (sub f), where v is the astronaut;s velocity and c is the speed of light.\r<BR>\n" );
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document.write( "a. Find lim_v-c R (sub a)<BR>\n" );
document.write( "b. If you are traveling in a starship at velocities approaching the speed of light, what does the limit in part a indicate about your aging rate relative to a friend on Earth?<BR>\n" );
document.write( "c. Explain why a left-hand limit is used in part a.\r<BR>\n" );
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document.write( "I know it's long but thanks for everyone's help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #113285 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=113285\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The formula: R (sub a) = R (sub f)sqrt{1-(v/c)^2} <BR>\n" );
document.write( "expresses the aging rate of an astronaut. R (sub a), relative to the aging rate of a friend on Earth, R (sub f), where v is the astronaut;s velocity and c is the speed of light. <BR>\n" );
document.write( "a. Find the limit as v goes to c of  R (sub a)<BR>\n" );
document.write( "As v goes to c (v/c) goes to 1; sqrt(1-(v/c)^2) goes to zero; R(sub a) goes<BR>\n" );
document.write( "to zero.<BR>\n" );
document.write( "b. If you are traveling in a starship at velocities approaching the speed of light, what does the limit in part a indicate about your aging rate relative to a friend on Earth?<BR>\n" );
document.write( "I stay young and the earthling ages.<BR>\n" );
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document.write( "c. Explain why a left-hand limit is used in part a.<BR>\n" );
document.write( "The left-hand limit will be positive implying there is some aging.<BR>\n" );
document.write( "A right-hand limit would be negative implying the space traveler<BR>\n" );
document.write( "was getting younger.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
document.write( " </SPAN>\n" );
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