A stone is projected with a velocity $20 \sqrt{2}\,m / s$ at an angle of $45^{\circ}$ to the horizontal. The average velocity of stone during its motion from starting point to its maximum height is $..........\,m/s$ (take $g=10\,m / s ^2$ )

A body of mass $0.5 \,kg$ is projected under gravity with a speed of $98 \,m/s$ at an angle of ${30^o}$ with the horizontal. The change in momentum (in magnitude) of the body is ......... $N-s$

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

A boy playing on the roof of a $10\, m$ high building throws a ball with a speed of $10\,m/s$ at an angle of $30^o$ with the horizontal. How far from the throwing point will the ball be at the height of $10\, m$ from the ground ?  $\left[ {g = 10\,m/{s^2},\sin \,{{30}^o} = \frac{1}{2},\cos \,{{30}^o} = \frac{{\sqrt 3 }}{2}} \right]$

Two projectile thrown at $30^{\circ}$ and $45^{\circ}$ with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is

A projectile thrown with velocity $v$ making angle $\theta$ with vertical gains maximum height $H$ in the time for which the projectile remains in air, the time period is