document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=996070>Question 996070</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If we neglect air resistance, then the range of a ball (or any projectile) shot at an angle &#952; with respect to the x axis and with an initial velocity v0, is given by \r<BR>\n" );
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document.write( "R(&#952;)=v_0^2/g sin(2&#952;) for 0 &#8804; &#952; &#8804; &#960;/2 \r<BR>\n" );
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document.write( "where g is the acceleration due to gravity (9.8 meters per second per second). \r<BR>\n" );
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document.write( "For what value of &#952; is the maximum range attained? (Note that the answer is numerical, not symbolic.) \r<BR>\n" );
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document.write( "&#952; =\r<BR>\n" );
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document.write( "Please explain<BR>\n" );
document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #614643 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=614643\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> R(theta) = (v0^2/g)*sin(2*theta)<BR>\n" );
document.write( "R ' (theta) = (v0^2/g)*2*cos(2*theta)<BR>\n" );
document.write( "0 = (v0^2/g)*2*cos(2*theta)<BR>\n" );
document.write( "cos(2*theta) = 0<BR>\n" );
document.write( "2*theta = arccos(0)<BR>\n" );
document.write( "2*theta = pi/2 + 2pi*n or 2*theta = -pi/2 + 2pi*n<BR>\n" );
document.write( "theta = pi/4 + pi*n or theta = -pi/4 + 2pi*n\r<BR>\n" );
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document.write( "Ignore the theta = -pi/4 + 2pi*n portion since the first part is negative pushing it out of the interval [0,pi/2]\r<BR>\n" );
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document.write( "Only one value of n will make theta = pi/4 + pi*n in the interval [0,pi/2]. This value of n is n = 0\r<BR>\n" );
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document.write( "If n = 0, then theta = pi/4\r<BR>\n" );
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document.write( "Final Answer: <font color=\"red\">pi/4 = 0.78539816339744</font> (decimal value is approximate)\r<BR>\n" );
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document.write( "pi/4 radians = 45 degrees<BR>\n" );
document.write( "This is halfway between 0 and 90 degrees </SPAN>\n" );
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