We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+5
1
941
3
avatar+284 

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+28182 
+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+28182 
+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+105606 
0

Yes, thank you very much Alan :)

 Nov 29, 2015

13 Online Users