Two particles are projected simultaneously from the same point, with the same speed, in the same vertical plane, and at different angles with the horizontal in a uniform gravitational field acting vertically downwards. A frame of reference is fixed to one particle. The position vector of the other particle, as observed from this frame, is $\overrightarrow{r}$. Which of the following statements is correct?

In the figure, the angle of inclination of the inclined plane is $30°$. Find the horizontal velocity $V_0$ so that the particle hits the inclined plane perpendicularly.

Two particles $A$ and $B$ are placed as shown in the figure.The particle $A$ on the top of tower, is projected horizontally with a velocity $u$ and particle $B$ is projected along the surface towards the tower, simultaneously. If both particles meet each other, then the speed of projection of particle $B$ is [ignore any friction]

A projectile is fired with a velocity $v$ at right angle to the slope inclined at an angle $\mathrm{\theta }$ with the horizontal. The range of the projectile along the inclined plane is

A cannon fires a projectile as shown in figure. The dashed line shows the trajectory in the absence of gravity. The points $M\text{,} N\text{,} O$ and $P$ correspond to time at, $t=0\text{,} 1 \mathrm{s}\text{,} 2 \mathrm{s}$ and $3 \mathrm{s}$, respectively. The lengths of $X\text{,} Y$ and $Z$ are, respectively,