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	<title>Comments on: A plane flying with a constant speed of km/min passes over a ground radar station at an altitude of km and c</title>
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		<title>By: Mark</title>
		<link>http://www.veryeasyflying.com/uncategorized/a-plane-flying-with-a-constant-speed-of-kmmin-passes-over-a-ground-radar-station-at-an-altitude-of-km-and-c/comment-page-1/#comment-2821</link>
		<dc:creator>Mark</dc:creator>
		<pubDate>Thu, 11 Mar 2010 18:52:41 +0000</pubDate>
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		<description>This is a related rates (calculus) problem.

Draw the picture.

See the right triangle.

Label the three sides:  The hypotenuse connects the station and the plane.  The horizontal side is at the plane&#039;s altitude; its length is (x km/hr)(a hrs)(cos theta).  The vertical side is directly above the station; it&#039;s length is the sum of the initial altitude (b km) plus (x km/hr)(a hrs)(sine theta).

The climb angle is theta.

The triangle is growing as the plane climbs.  Each side is lengthening.  You want to know the rate at which the hypotenuse is increasing.  (D/dt hypotenuse). 

Show the three sides as a Pythagorean relation.

hypotenuse² =  horizontal side² + vertical side².

hypotenuse = ?(horizontal side² + vertical side²).

D/dt hypotenuse = D/dt?(horizontal side² + vertical side²).

Use IMPLICIT differentiation.  Look at that chapter.  Use the chain rule.  Use the product rule.  Be careful with signs of trig derivatives.  Expand.  Simplify.</description>
		<content:encoded><![CDATA[<p>This is a related rates (calculus) problem.</p>
<p>Draw the picture.</p>
<p>See the right triangle.</p>
<p>Label the three sides:  The hypotenuse connects the station and the plane.  The horizontal side is at the plane&#8217;s altitude; its length is (x km/hr)(a hrs)(cos theta).  The vertical side is directly above the station; it&#8217;s length is the sum of the initial altitude (b km) plus (x km/hr)(a hrs)(sine theta).</p>
<p>The climb angle is theta.</p>
<p>The triangle is growing as the plane climbs.  Each side is lengthening.  You want to know the rate at which the hypotenuse is increasing.  (D/dt hypotenuse). </p>
<p>Show the three sides as a Pythagorean relation.</p>
<p>hypotenuse² =  horizontal side² + vertical side².</p>
<p>hypotenuse = ?(horizontal side² + vertical side²).</p>
<p>D/dt hypotenuse = D/dt?(horizontal side² + vertical side²).</p>
<p>Use IMPLICIT differentiation.  Look at that chapter.  Use the chain rule.  Use the product rule.  Be careful with signs of trig derivatives.  Expand.  Simplify.</p>
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	<item>
		<title>By: Waz</title>
		<link>http://www.veryeasyflying.com/uncategorized/a-plane-flying-with-a-constant-speed-of-kmmin-passes-over-a-ground-radar-station-at-an-altitude-of-km-and-c/comment-page-1/#comment-2820</link>
		<dc:creator>Waz</dc:creator>
		<pubDate>Thu, 11 Mar 2010 17:57:41 +0000</pubDate>
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		<description>Im sorry? I think you&#039;ve missed some number out...</description>
		<content:encoded><![CDATA[<p>Im sorry? I think you&#8217;ve missed some number out&#8230;</p>
]]></content:encoded>
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