Airplanes $A$ and $B$ are flying with constant velocity in the same vertical plane at angles $30°$ and $60°$ with respect to the horizontal respectively as shown in the figure. The speed of $A$ is $100\sqrt{3}{ \mathrm{m} \mathrm{s}}^{-1}$. At time $t=0 \mathrm{s}\text{,}$ an observer in $A$ finds $B$ at a distance of $500 \mathrm{m}.$ This observer sees $B$ moving with a constant velocity perpendicular to the line of motion of $A.$ If at $t=t_0, A$ just escapes being hit by $B, t_0$ in seconds is