document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204112>Question 1204112</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Word Problem Create a mch Find the matart vector in each problem and direction\r<BR>\n" );
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document.write( "1. An airplane is flying 340 km/hr at 12° North of Pan. The wind is blowing 40 km at 34° South of East What is the plane actual velocity? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848012 by </B><A HREF=/tutors/aboutme.mpl?userid=asinus><B>asinus(45)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=asinus><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=848012\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Define the Coordinate System**\r<BR>\n" );
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document.write( "* Let's define our coordinate system with:<BR>\n" );
document.write( "    * **East as the positive x-axis**<BR>\n" );
document.write( "    * **North as the positive y-axis**\r<BR>\n" );
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document.write( "**2. Resolve the Velocities into Components**\r<BR>\n" );
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document.write( "* **Plane's Velocity:**<BR>\n" );
document.write( "    * Magnitude: 340 km/hr<BR>\n" );
document.write( "    * Direction: 12° North of East <BR>\n" );
document.write( "        * x-component: 340 * cos(12°) = 332.54 km/hr (East)<BR>\n" );
document.write( "        * y-component: 340 * sin(12°) = 70.43 km/hr (North)\r<BR>\n" );
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document.write( "* **Wind Velocity:**<BR>\n" );
document.write( "    * Magnitude: 40 km/hr<BR>\n" );
document.write( "    * Direction: 34° South of East <BR>\n" );
document.write( "        * x-component: 40 * cos(34°) = 33.14 km/hr (East)<BR>\n" );
document.write( "        * y-component: -40 * sin(34°) = -22.36 km/hr (South)\r<BR>\n" );
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document.write( "**3. Calculate the Resultant Velocity**\r<BR>\n" );
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document.write( "* **Resultant x-component:** 332.54 km/hr (plane) + 33.14 km/hr (wind) = 365.68 km/hr<BR>\n" );
document.write( "* **Resultant y-component:** 70.43 km/hr (plane) - 22.36 km/hr (wind) = 48.07 km/hr\r<BR>\n" );
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document.write( "**4. Calculate the Magnitude of the Resultant Velocity**\r<BR>\n" );
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document.write( "* Magnitude = √(x-component² + y-component²) <BR>\n" );
document.write( "* Magnitude = √(365.68² + 48.07²) <BR>\n" );
document.write( "* Magnitude ≈ 369.45 km/hr\r<BR>\n" );
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document.write( "**5. Calculate the Direction of the Resultant Velocity**\r<BR>\n" );
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document.write( "* Direction = arctan(y-component / x-component)<BR>\n" );
document.write( "* Direction = arctan(48.07 / 365.68) <BR>\n" );
document.write( "* Direction ≈ 7.48° North of East\r<BR>\n" );
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document.write( "**Therefore:**\r<BR>\n" );
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document.write( "* **Magnitude of the plane's actual velocity:** 369.45 km/hr<BR>\n" );
document.write( "* **Direction of the plane's actual velocity:** 7.48° North of East\r<BR>\n" );
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document.write( "**In summary:**\r<BR>\n" );
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document.write( "The plane's actual velocity is 369.45 km/hr at a direction of 7.48° North of East, taking into account the effect of the wind.<BR>\n" );
document.write( " </SPAN>\n" );
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