$A$ body of mass $m$ is thrown upwards at an angle $\theta$ with the horizontal with velocity $v$. While rising up,the velocity of the mass after $t$ seconds will be:

In a spring gun having a spring constant $k = 100\, \text{N/m}$,a small ball $B$ of mass $m = 100\, \text{g}$ is placed in its barrel (as shown in the figure) by compressing the spring by $x = 0.05\, \text{m}$. $A$ box is placed at a distance $d$ on the ground so that the ball falls into it. If the ball leaves the gun horizontally at a height of $h = 2\, \text{m}$ above the ground,find the value of $d$ in meters. (Take $g = 10\, \text{m/s}^2$)

The angle of projection of a projectile for which its initial kinetic energy becomes half at its maximum height is (in $^{\circ}$)

$A$ bullet is fired with a velocity $u$ making an angle of $60^{\circ}$ with the horizontal plane. The horizontal component of the velocity of the bullet when it reaches the maximum height is

Three identical balls are projected with the same speed at angles $30^{\circ}$,$45^{\circ}$,and $60^{\circ}$. Their ranges are $R_1$,$R_2$,and $R_3$ respectively. Then:

$A$ particle is projected with speed $u$ at an angle $\theta$ with the horizontal from the ground. If it is at the same height from the ground at times $t_1$ and $t_2$,then its average velocity in the time interval $t_1$ to $t_2$ is .........