+286 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?
+33661 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.
+33661 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.
