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,

Shots are fired simultaneously from the top and bottom of a vertical cliff with the elevation $\alpha =30°, \beta =60°$, respectively (figure). The shots strike an object simultaneously at the same point. If $a=30\sqrt{3} \mathrm{m}$ is the horizontal distance of the object from the cliff, then the height $h$ of the cliff is

figure shows that particle $A$ is projected from point $P$. with velocity $u$ along the plane and simultaneously another particle $B$ with velocity $v$ at an angle $\alpha$ with vertical. The particles collide at point $Q$ on the plane. Then