Difference between revisions of "007A Sample Midterm 2, Problem 5 Detailed Solution"

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(Created page with "<span class="exam"> 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 s...")
 
 
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[[007A_Sample_Midterm_2|'''<u>Return to Sample Exam</u>''']]
 
[[007A_Sample_Midterm_2|'''<u>Return to Sample Exam</u>''']]

Latest revision as of 11:42, 5 January 2018

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?


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

        hypotenuse, we have  


Step 1:  
9AF 5 GP.png
From the diagram, we have    by the Pythagorean Theorem.
Taking derivatives, we get

       

Step 2:  
If     then
       
So, we have
       
Solving for     we get    


Final Answer:  
        

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