A ball is projected at an angle of $30°$ above with the horizontal from the top of a tower and strikes the ground in $5 \mathrm{s}$ at an angle of $45°$ with the horizontal. Find the speed with which it was projected.

Two balls of mass $M$ and $2M$ are thrown horizontally with the same initial velocity $v_0$ from top of a tall tower and experience a drag force of $-kv\left(k>0\right)$ where $v$ is the instantaneous velocity.

Then,

A bomber plane moving at a horizontal speed of $20 \mathrm{m} {\mathrm{s}}^{-1}$ releases a bomb at a height of $80 \mathrm{m}$ above ground as shown. At the same instant, a hunter of negligible height starts running from a point below it, to catch the bomb with speed $10 \mathrm{m} {\mathrm{s}}^{-1}$. After two seconds he realised that he cannot make it, he stops running and immediately holds his gun and fires in such a direction, so that just before the bomb hits the ground, a bullet will hit it. What should be the firing speed of bullet. (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$ )

A spot light $S$ rotates in a horizontal plane with a constant angular velocity of $0.1 \mathrm{rad} {\mathrm{s}}^{-1}$. The spot of light $P$ moves along the wall at a distance $3 \mathrm{m}$. What is the velocity of the spot $P$ when $\mathrm{\theta } = 45°$?

Two identical discs of the same radius $R$ are rotating about their axes in opposite directions with the same constant angular speed $\omega$. The disc is in the same horizontal plane.At time $t\mathit{ }= 0$, the points $P$ and $Q$ are facing each other as shown in the figure. The relative speed between the two points $P$ and $Q$ is $v_{\mathit{r}}$ as a function of times best represented by

 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.