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

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!Step 1:    
 
!Step 1:    
 
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|Insert diagram.
 
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|From the diagram, we have <math>30^2+h^2=s^2</math> by the Pythagorean Theorem.
 
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|Taking derivatives, we get
 
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|<math>2hh'=2ss'</math>.
 
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!Step 2: &nbsp;
 
!Step 2: &nbsp;
 
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|If <math>s=50</math>, then <math>h=\sqrt{50^2-30^2}=40</math>.
 
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|So, we have <math>2(40)6=2(50)s'</math>.
 
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|Solving for <math>s'</math>, we get <math>s'=\frac{24}{5} </math>m/s.
 
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!Final Answer: &nbsp;  
 
!Final Answer: &nbsp;  
 
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| <math>s'=\frac{24}{5} </math>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 11:30, 15 February 2016

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:  

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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