Two ships $A$ and $B$ can establish mutual communication when they are not more than $50 \mathrm{km}$ apart. At midnight, the ship $B$ moving towards north with a constant velocity of $4 {\mathrm{kmhr}}^{-1}$ passes a location $80\mathrm{km}$ east of ship A, that is moving with a constant velocity of $16\sqrt{2} {\mathrm{kmhr}}^{-1}$ towards northeast. If time interval (in seconds) for which they remain in communication is $x\times {10}^2\mathrm{S}$, find $x$.

The time period of a particle $P$ moving along a circular path of radius $1 \mathrm{cm}$ is $\pi s.$  Another particle $Q$ starts from rest at a point $A$ and travelling along a straight line path reaches the point $B$ in $2 \mathrm{s}$. If $AB=12 \mathrm{cm}$ and the particles $P$ and $Q$ are respectively at $D$ and $B$ at an instant shown in the figure, the acceleration of particle $Q$ with respect to particle $P$ is _______$\mathrm{cm} {\mathrm{s}}^{-2}$. (Points $A\mathit{,}B\mathit{,}C\mathit{,}D$ and $O$ lie along the same straight line)

A swimmer wants to cross a river from point $A$ to point $B$. Line AB makes an angle of $30°$ with the flow of the river. The magnitude of the velocity of the swimmer is the same as that of the river. The angle $\theta$ with the line $AB$ should be _______$°$, so that the swimmer reaches point $B$.