Difference between revisions of "009A Sample Final 1, Problem 5"

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!Foundations:    
 
!Foundations:    
 
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|Recall:
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|'''The Pythagorean Theorem'''
 
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|'''The Pythagorean Theorem:''' For a right triangle with side lengths <math style="vertical-align: -4px">a,b,c</math>, where <math style="vertical-align: 0px">c</math> is the length of the  
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|&nbsp; &nbsp; &nbsp; &nbsp; For a right triangle with side lengths <math style="vertical-align: -4px">a,b,c</math>, where <math style="vertical-align: 0px">c</math> is the length of the  
 
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::hypotenuse, we have <math style="vertical-align: -2px">a^2+b^2=c^2.</math>
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&nbsp; &nbsp; &nbsp; &nbsp; hypotenuse, we have <math style="vertical-align: -2px">a^2+b^2=c^2.</math>
 
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::<math>2hh'=2ss'.</math>
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&nbsp; &nbsp; &nbsp; &nbsp; <math>2hh'=2ss'.</math>
 
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!Step 2: &nbsp;
 
!Step 2: &nbsp;
 
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|If&thinsp; <math style="vertical-align: -4px">s=50,</math> then&thinsp; <math style="vertical-align: -2px">h=\sqrt{50^2-30^2}=40.</math>
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|If &nbsp; <math style="vertical-align: -4px">s=50,</math> then&thinsp; <math style="vertical-align: -2px">h=\sqrt{50^2-30^2}=40.</math>
 
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|So, we have&thinsp; <math style="vertical-align: -5px">2(40)6=2(50)s'.</math>
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|So, we have &nbsp; <math style="vertical-align: -5px">2(40)6=2(50)s'.</math>
 
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|Solving for&thinsp; <math style="vertical-align: -5px">s',</math> we get&thinsp; <math style="vertical-align: -14px">s'=\frac{24}{5}</math>&thinsp; m/s.
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|Solving for &nbsp; <math style="vertical-align: -5px">s',</math>&nbsp;  we get &nbsp; <math style="vertical-align: -14px">s'=\frac{24}{5}</math> &nbsp; m/s.
 
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!Final Answer: &nbsp;  
 
!Final Answer: &nbsp;  
 
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|&nbsp; &nbsp; &nbsp; &nbsp;<math style="vertical-align: -14px">s'=\frac{24}{5}</math>&nbsp; m/s
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:<math style="vertical-align: -14px">s'=\frac{24}{5}</math>&thinsp; m/s
 
 
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[[009A_Sample_Final_1|'''<u>Return to Sample Exam</u>''']]
 
[[009A_Sample_Final_1|'''<u>Return to Sample Exam</u>''']]

Revision as of 17:41, 25 February 2017

A kite 30 (meters) above the ground moves horizontally at a speed of 6 (m/s). At what rate is the length of the string increasing

when 50 (meters) of the string has been let out?

Foundations:  
The Pythagorean Theorem
        For a right triangle with side lengths , where is the length of the

        hypotenuse, we have


Solution:

Step 1:  
Insert diagram.
From the diagram, we have by the Pythagorean Theorem.
Taking derivatives, we get

       

Step 2:  
If   then 
So, we have  
Solving for     we get     m/s.


Final Answer:  
         m/s

Return to Sample Exam

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