A rod of length 13 metres 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 the speed of 12 m/sec, then the speed of the other end Q when it is 12 m from the origin is
Answer & explanation
Correct answer: option 3
$x^2+y^2=(13)^2=169$
$\Rightarrow 2 x \frac{d x}{d t}+2 y \frac{d y}{d t}=0$
$\Rightarrow x \frac{d x}{d t}+y \frac{d y}{d t}=0$
$\frac{d x}{d t}$ = 12 (given)
$\Rightarrow x \frac{d x}{d t}+y \frac{d y}{d t}=0$
But, y = 12 (given) $\Rightarrow x^2+144=169 \Rightarrow x^2=25 \Rightarrow x=5$
∴ $\left.\frac{d y}{d t}\right|_{y=12}=\frac{-12(5)}{12}=-5$
∴ speed of Q = –5 m/sec.