On an inclined plane, two particles $A$ and $B$ are projected with the same speed at the same angle with the horizontal, particle $A$ down and particle $B$ up the plane. If the ratio of time of flight of $A$ and $B$ is $\cot \theta$ where $\theta$ is the angle at which  $B$ 

Two balls are thrown from an inclined plane at an angle of projection $\mathrm{\alpha }$ with the plane, one up the incline plane and the other down the incline as shown in the figure. If $R_1$ and $R_2$ are their respective ranges, then ($T_1$ and $T_2$ are times of flight in the two cases, respectively)

A river is flowing from east to west at a speed of $5 \mathrm{m} {\min }^{-1}$. A man on the south bank of river, capable of swimming $10 \mathrm{m} {\min }^{-1}$ in still water, wants to swim across the river in the shortest time. He should swim

A boat is rowed across a river at a rate of $4.5 \mathrm{km} {\mathrm{hr}}^{-1}$. The river flows at the rate of $6 \mathrm{km} {\mathrm{hr}}^{-1}$. The velocity of the boat in $\mathrm{m} {\mathrm{s}}^{-1}$ is