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?
Assuming P = (x, 0) and Q = (0, y)
x2+y2=132
Differentiate with respect to time
2xdxdt+2ydydt=0
Substitute 12 for dx/dt and for y and rearrange
dydt=−12x12=−x
Use the first equation above to replace x
dydt=−√132−122=−5
So Q moves at 5 m/s down the y-axis.
Thank you very much!
Yes, thank you very much Alan :)
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