document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=773627>Question 773627</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, I've had trouble solving this word problem...\"At the ocean it is known that the tide follows a trigonometric path. At high tide, the water comes in to a point 1 meter from where I placed the flag. At low tide, the water comes in to a point 11 meters from the same flag. The time it takes from to get from high tide to low tide is 5 hours. It is now midnight and it is high tide.<BR>\n" );
document.write( "a) State a possible equation for this motion.<BR>\n" );
document.write( "b) We want to wake up and go to the beach when we can set up our towels at a time between 10 a.m. and 2 p.m. the next day when the water will be 4 meters from our flag. At what time will this be?\"<BR>\n" );
document.write( "I've figured out that the low tide is the maximum and the high tide is the minimum but I don't know how to proceed...Help? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #471716 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=471716\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ...\"At the ocean it is known that the tide follows a trigonometric path. At high tide, the water comes in to a point 1 meter from where I placed the flag. At low tide, the water comes in to a point 11 meters from the same flag. The time it takes from to get from high tide to low tide is 5 hours. It is now midnight and it is high tide.<BR>\n" );
document.write( "a) State a possible equation for this motion.<BR>\n" );
document.write( "The period is 10 hours.<BR>\n" );
document.write( "The amplitude is 10 meters<BR>\n" );
document.write( "h(t) = 10sin(2pi*t/10)<BR>\n" );
document.write( "h(t) = 10sin(pi*t/5), t in hours, h in meters<BR>\n" );
document.write( "Measured from the flag, it's <BR>\n" );
document.write( "h(t) = 10sin(pi*t/5) + 1<BR>\n" );
document.write( "That gives a sinusoidal motion from 1 m to 11 m from the flag, with t = 0 at midnight.<BR>\n" );
document.write( "------<BR>\n" );
document.write( "b) We want to wake up and go to the beach when we can set up our towels at a time between 10 a.m. and 2 p.m. the next day when the water will be 4 meters from our flag. At what time will this be?<BR>\n" );
document.write( "h(t) = 10sin(pi*t/5) + 1 = 4<BR>\n" );
document.write( "10sin(pi*t/5) =  3<BR>\n" );
document.write( "sin(pi*t/5) =  0.3<BR>\n" );
document.write( "pi*t/5 =~ 0.305<BR>\n" );
document.write( "t = 0.305*5/pi hours after midnight<BR>\n" );
document.write( "t =~ 0.484 hours > midnight = 0029<BR>\n" );
document.write( "t = pi - 0.484 = 2.657 hours > midnight = 0239, still too early<BR>\n" );
document.write( "The period is 10 hours, so it's at 4 meters again at 1029 & 1239<BR>\n" );
document.write( "Its distance from the flag increases from 4 meters at 1029 as the tide goes out, then is at 4 meters from the flag at 1239 as the tide comes in.<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "PS  The water level is highest at high tide, lowest at low tide (measured from the bottom).<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );