Answer
$-5\frac{m}{sec}$
Work Step by Step
Given: $\frac{dx}{dt}=-1\frac{m}{sec},\frac{dy}{dt}=-5\frac{m}{sec}$
$x=5,y=12$
Whenever the variables of two coordinates are differentiable with respect to time, the distance from the origin to that point will be a straight line.
We apply the Pythagorean Theorem:
$s^2=x^2+y^2$
$s=\sqrt{(5^2+12^2)}=13$
on applying differentiation, we get:
$2s\frac{ds}{dt}=2x\frac{dx}{dt}+2y\frac{dy}{dt}$
$\frac{ds}{dt}=\frac{1}{s}(x\frac{dx}{dt}+y\frac{dy}{dt})$
$\frac{ds}{dt}=\frac{1}{13}(5(-1)+12(-5))=-5\frac{m}{sec}$
Thus, the final answer is: $-5\frac{m}{sec}$
