The range of the projectile projected at an angle of $15^{\circ}$ with the horizontal is $50\,m$. If the projectile is projected with the same velocity at an angle of $45^{\circ}$ with the horizontal,then its range will be $........\,m$.

$A$ ball is projected from a building of height $10 \ m$ with a velocity of $10 \ m/s$ at an angle of $30^\circ$ with the horizontal. What is the horizontal distance covered by the ball when it reaches the same height of $10 \ m$ again (in $m$)? $(g = 10 \ m/s^2, \sin 30^\circ = 1/2, \cos 30^\circ = \sqrt{3}/2)$

$A$ ball projected at an angle of $45^{\circ}$ with the horizontal crosses two points at equal heights separated by a distance at times $2 \ s$ and $8 \ s$ respectively. The horizontal distance between the two points is (Acceleration due to gravity $= 10 \ m/s^2$) (in $m$)

$A$ projectile is thrown at a speed which is twice its speed at its maximum height. If $R$ and $H$ are its range and maximum height respectively, then the ratio $\frac{R}{H}$ is

Four projectiles are fired with the same velocities at angles $25^{\circ}, 40^{\circ}, 55^{\circ}$ and $70^{\circ}$ with the horizontal. The range of the projectile will be largest for the one projected at angle $.......$ . (in $^{\circ}$)

$A$ particle is projected from a horizontal plane such that its velocity vector at time $t$ is given by $\vec{v} = a\hat{i} + (b - ct)\hat{j}$. Its range on the horizontal plane is given by