Answer
$2$ m/sec.
Work Step by Step
Step 1. Identify the given conditions: $x'=\frac{dx}{dt}=10m/sec, y'=\frac{dy}{dt}=5m/sec$, point $(3,-4)$
Step 2. Calculate the distance of the point to the origin: $s=\sqrt {x^2+y^2}=\sqrt {3^2+(-4)^2}=5$
Step 3. Take derivatives: $s^2=x^2+y^2$, $2ss'=2xx'+2yy'$, thus $\frac{ds}{dt}=s'=\frac{xx'+yy'}{s}=\frac{3(10)+(-4)(5)}{5}=\frac{10}{5}=2$ m/sec (positive means moving away from the origin)
