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هاله
01-02-2004, 04:15 PM
a missile is fired vertically from apoint that is 5 mi from a tracking station and at the same elevation . for the first 20 sec of flight,its angle of elevation changes at aconstant rate of 2 per second.find the velocity of the missile when the angle of elevation is 30

:)

uaemath
02-02-2004, 10:48 AM
The rate of change of the angle A is :


<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "81" height = "40" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "DIV(dA;dt)=SUP(2;o)/sec"></applet></html>
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "111" height = "35" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "= DIV(SYMBOL_73;90) radians /sec"></applet></html>
http://www.mathyards.com/hala.GIF

tanA = y/5 <=> y = 5 tan A
differentiate with respect to time
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "139" height = "40" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "DIV(dy;dt)=(5SUP(sec;2)A)(DIV(dA;dt))"></applet></html>
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "255" height = "54" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "When A = SUP(30;o)=DIV(SYMBOL_73;6) ,SUP(sec;2)A =SUP((DIV(2;ROOT(2)));2)=DIV(4;3)"></applet></html>
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "249" height = "40" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "Hence DIV(dy;dt)= 5(DIV(4;3))(DIV(SYMBOL_73;90))=DIV(2SYMBOL_73;27) miles/sec"></applet></html>