Two men, $P$ and $Q$ are standing at corners $A$ and $B$ of a square $ABCD$ of side $8 \mathrm{m}$. They start moving along the track with constant speed $2 \mathrm{m} {\mathrm{s}}^{-1}$ and $10 \mathrm{m} {\mathrm{s}}^{-1}$, respectively. Find the time when they will meet for the first time.

 

$P$ is a point moving with a constant speed $10 \mathrm{m} {\mathrm{s}}^{-1}$ such that its velocity vector always maintains an angle $60°$ with the line $OP$, as shown in the figure (where $O$ is a fixed point in space). The initial distance between $O$ and $P$ is $100 \mathrm{m}$. After what time (in $\sec$) shall $P$ reach $O$? 

A train of length $210 \mathrm{m}$ is moving with a speed of $25 \mathrm{m} {\mathrm{s}}^{-1}$ in North direction. A small bird is flying above the train with a speed of $5 \mathrm{m} {\mathrm{s}}^{-1}$ in south direction. Find the time taken by the bird to cross the train in seconds.

A boy standing on the foothpath tosses a ball straight up and catches it. The driver of a car passing by moving with uniform velocity sees this.

The trajectory of the ball as seen by the driver will be