+0

# Calculus question

+5
396
3
+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?

buubleman  Nov 25, 2015

#1
+26322
+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
Sort:

#1
+26322
+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
#2
+284
+5

Thank you very much!

buubleman  Nov 27, 2015
#3
+90988
0

Yes, thank you very much Alan :)

Melody  Nov 29, 2015

### 7 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details