$A$ projectile is launched from the ground, such that it hits a target on the ground which is $90 \,m$ away. The minimum velocity of the projectile to hit the target is (acceleration due to gravity $= 10 \,ms^{-2}$) (in $\,ms^{-1}$)

$A$ body is projected with a velocity $(\hat{i} + 2\hat{j}) \text{ ms}^{-1}$,where $\hat{i}$ is along the horizontal and $\hat{j}$ is vertically upward. Then the equation of its trajectory is $(g = 10 \text{ ms}^{-2})$.

Two balls $A$ and $B$ are projected at an angle of $45^{\circ}$ and $60^{\circ}$ respectively, so that the maximum heights reached are same for both. The ratio of initial velocity of projection of ball $A$ to that for ball $B$ is $(\sin 30^{\circ} = \cos 60^{\circ} = 1/2, \sin 45^{\circ} = \cos 45^{\circ} = 1/\sqrt{2}, \sin 60^{\circ} = \cos 30^{\circ} = \sqrt{3}/2)$.

Two objects are thrown up at angles of $45^{\circ}$ and $60^{\circ}$ respectively,with the horizontal. If both objects attain the same vertical height,then the ratio of the magnitude of velocities with which these are projected is .........

$A$ body is projected with a speed $u \ m/s$ at an angle $\beta$ with the horizontal. The kinetic energy at the highest point is $3/4$ of the initial kinetic energy. The value of $\beta$ is: (in $^{\circ}$)

The maximum horizontal range of a projectile is $160 \ m$. When the projectile is thrown with the same speed at an elevation of $30^{\circ}$ from the horizontal,it will reach a maximum height of ......... $m$.