$A$ particle is projected with a velocity of $30\,m/s$ at an angle of $\theta_0 = \tan^{-1}(3/4)$. After $1\,s$,the particle is moving at an angle $\theta$ to the horizontal. What is the value of $\tan\theta$? (Take $g = 10\,m/s^2$)

$A$ stone is projected from the ground with velocity $50 \, m/s$ at an angle of $30^o$. It crosses a wall after $3 \, s$. How far beyond the wall will the stone strike the ground? $(g = 10 \, m/s^2)$

$A$ projectile thrown from the ground has initial speed $u$ and its direction makes an angle $\theta$ with the horizontal. If at maximum height from the ground,the speed of the projectile is half its initial speed of projection,then the maximum height reached by the projectile is:
$[g = \text{acceleration due to gravity}, \sin 30^{\circ} = \cos 60^{\circ} = 0.5, \cos 30^{\circ} = \sin 60^{\circ} = \sqrt{3}/2]$

The horizontal and vertical displacements $x$ and $y$ of a projectile at a given time $t$ are given by $x = 6t \text{ m}$ and $y = 8t - 5t^2 \text{ m}$. The range of the projectile in metres is:

The maximum height attained by a projectile is increased by $10 \%$ by keeping the angle of projection constant. What is the percentage increase in the time of flight (in $\%$)?

$A$ projectile is thrown with an initial velocity of $10 \ m/s$ at an angle $\alpha$ with the horizontal. It has a range of $5 \ m$. Taking $g = 10 \ m/s^2$ and neglecting air resistance, what will be the estimated value of $\alpha$ (in $^{\circ}$)?