If the range of a body projected with a velocity of $60 \,m \,s^{-1}$ is $180 \sqrt{3} \,m$, then the angle of projection of the body is (Acceleration due to gravity $= 10 \,m \,s^{-2}$)

$A$ ball is thrown at an angle $\theta$ with the horizontal. Its horizontal range is equal to its maximum height. This is possible only when the value of $\tan \theta$ is ..........

From the top of a tower,$80 \ m$ high from the ground,a stone is thrown in the horizontal direction with a velocity of $8 \ ms^{-1}$. The stone reaches the ground after a time $t$ and falls at a distance of $d$ from the foot of the tower. Assuming $g=10 \ ms^{-2}$,the time $t$ and distance $d$ are given respectively by

$A$ particle is projected at an angle of $45^{\circ}$ with the horizontal with an initial kinetic energy $K$. What will be its kinetic energy at the highest point?

$A$ ball is projected vertically upwards with a certain initial speed. Another ball of the same mass is projected with the same speed at an angle of $30^{\circ}$ with the horizontal. At the highest point,the ratio of their potential energies is

The equation of trajectory of a projectile is $y = 10x - (5/9)x^2$. If we assume $g = 10 \ m/s^2$,the range of the projectile (in meters) is: