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Calculus question

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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

#1
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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
+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.

Alan Nov 27, 2015
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Thank you very much!

Nov 27, 2015
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Yes, thank you very much Alan :)

Nov 29, 2015