$A$ ball thrown by one player reaches the other in $2 \, s$. The maximum height attained by the ball above the point of projection will be about .......... $m$.

$A$ projectile is thrown with an initial velocity of $(a \hat{i} + b \hat{j}) \text{ m s}^{-1}$. If the range of the projectile is twice the maximum height reached by it,then

$A$ projectile is projected from the ground with an initial velocity $\vec{u} = u_0 \hat{i} + v_0 \hat{j}$. If the acceleration due to gravity $g$ is along the negative $y$-direction,find the maximum displacement in the $x$-direction (horizontal range).

$A$ heavy particle is projected from a point on the horizontal at an angle $60^\circ$ with the horizontal with a speed of $10 \ m/s$. Then the radius of curvature of its path at the instant of crossing the same horizontal will be ......... $m$.

$A$ small ball is thrown at an angle $45^{\circ}$ to the horizontal with an initial velocity of $2 \sqrt{2} \ m/s$. The magnitude of the mean velocity averaged over the first $2 \ s$ is (take acceleration due to gravity $g = 10 \ m/s^2$). (in $m/s$)

$A$ stone is thrown at an angle $\theta$ to the horizontal reaches a maximum height $H$. Then the time of flight of the stone will be