Airplanes $A$ and $B$ are flying with constant velocity in the same vartical plane at angle $30°$ and $60°$ with respect to the horizontal respectively as shown in Fig. The speed of $100 \sqrt{3} {\mathrm{ms}}^{-1}$. At time $t=0$, an observer in $A$ finds $B$ at 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 $B$, then find $t_0$ in seconds.

The length of a chamber inside the rocket is $4 \mathrm{m}$. A ball is thrown from the left end of the chamber in $+x$ direction with a speed of $0.3 {\mathrm{ms}}^{-1}$ relative to the rocket. At the same time, another ball is thrown in $-x$ direction with a speed of $0.2 {\mathrm{ms}}^{-1}$ from its right end relative to the rocket. Find time in seconds when the two balls hit each other. Give your answer to the nearest integer.

An object, moving with a speed of $6.25 \mathrm{m} {\mathrm{s}}^{-1}$, is decelerated at a rate given by $\frac{dv}{dt}=-2.5\sqrt{v}$, where $\nu$ is the instantaneous speed. The time taken by the object, to come to rest, would be: