The maximum range of a projectile is $500 \mathrm{m}$. If the particle is thrown up a plane which is inclined at an angle of $30°$ with the same speed, the distance covered by it along the inclined plane will be,

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

Two balls are projected from points $A$ and $B$ in vertical plane as shown in figure. $AB$ is a straight vertical line. The balls can collide in mid-air if $\frac{v_1}{v_2}$ is equal to,

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