$A$ bullet is fired with a speed of $1000 \, m/s$ in order to hit a target $100 \, m$ away. If $g = 10 \, m/s^2$,the gun should be aimed:

$A$ batsman hits a ball with a velocity '$v$',making an angle of $60^{\circ}$ with the vertical. After some time, the direction of velocity makes an angle of $60^{\circ}$ with the horizontal. The speed of the ball at this instant is $[\cos(60^{\circ}) = \frac{1}{2}, \cos(30^{\circ}) = \frac{\sqrt{3}}{2}]$.

$A$ body is projected from the earth at an angle of $30^{\circ}$ with the horizontal with some initial velocity. If its range is $20 \ m$, the maximum height reached by it is: (in meters)

$A$ body is projected with a speed $u \ m/s$ at an angle $\beta$ with the horizontal. The kinetic energy at the highest point is $3/4$ of the initial kinetic energy. The value of $\beta$ is: (in $^{\circ}$)

If a body is projected with an angle $\theta$ to the horizontal, then