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A rod of length 13 meters has one end P on the x-axis and the other end Q on the y-axis. If P moves on the x-axis with a velocity of 12 meters per second, then what is the velocity of the other end Q when it is 12 meters from the origin?

 Nov 25, 2015

Best Answer 

 #1
avatar+30021 
+10

Assuming P = (x, 0) and Q = (0, y)

 

\(x^2+y^2=13^2\)

 

Differentiate with respect to time

 

\(2x\frac{dx}{dt}+2y\frac{dy}{dt}=0\)

 

Substitute 12 for dx/dt and for y and rearrange

 

\(\frac{dy}{dt}= -12\frac{x}{12}=-x\)

 

Use the first equation above to replace x

 

\(\frac{dy}{dt}=-\sqrt{13^2-12^2}=-5\)

 

So Q moves at 5 m/s down the y-axis.

 Nov 27, 2015
 #1
avatar+30021 
+10
Best Answer

Assuming P = (x, 0) and Q = (0, y)

 

\(x^2+y^2=13^2\)

 

Differentiate with respect to time

 

\(2x\frac{dx}{dt}+2y\frac{dy}{dt}=0\)

 

Substitute 12 for dx/dt and for y and rearrange

 

\(\frac{dy}{dt}= -12\frac{x}{12}=-x\)

 

Use the first equation above to replace x

 

\(\frac{dy}{dt}=-\sqrt{13^2-12^2}=-5\)

 

So Q moves at 5 m/s down the y-axis.

Alan Nov 27, 2015
 #2
avatar+284 
+5

Thank you very much!

 Nov 27, 2015
 #3
avatar+109512 
0

Yes, thank you very much Alan :)

 Nov 29, 2015

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