A sitting cat in a field suddenly sees a standing dog. To save its life the cat runs away in a straight horizontal line with constant velocity  $\left(\overrightarrow{u}\right)$ 5m/s. Without any time lag the dog starts with velocity  $\left(\overrightarrow{v}\right)$ 10m/s constant in magnitude and always directed towards the cat to catch it. Initially,  $\overrightarrow{u}$  and  $\overrightarrow{v}$ are perpendicular and separation between the cat and the dog is 100m(as shown in figure).The time after which the dog catches the cat is  

$\frac{x}{3}$ sec, then x is