$A$ particle is projected at $60^{\circ}$ to the horizontal with a kinetic energy $K$. The kinetic energy at the highest point is

$A$ particle is projected at an angle of $30^{\circ}$ from the horizontal at a speed of $60 \; m/s$. The height traversed by the particle in the first second is $h_0$ and the height traversed in the last second before it reaches the maximum height is $h_1$. The ratio $h_0 : h_1$ is . . . . . . . [Take $g = 10 \; m/s^2$]

When a ball is thrown with a velocity of $50 \ m s^{-1}$ at an angle $30^{\circ}$ with the horizontal,it remains in the air for how many seconds? (Take $g = 10 \ m s^{-2}$)

The maximum horizontal range of a projectile is $16 \ km$. When the projectile is thrown at an elevation of $30^o$ from the horizontal,it will reach a maximum height of ....... $km$.

Two stones having different masses $m_1$ and $m_2$ are projected at an angle $\alpha$ and $(90^{\circ}-\alpha)$ with the same speed from the same point. The ratio of their maximum heights is

$A$ ball at point '$O$' is at a horizontal distance of $7 \ m$ from a wall. On the wall,a target is set at point '$C$'. If the ball is thrown from '$O$' at an angle $37^{\circ}$ with the horizontal,aiming at the target '$C$',but it hits the wall at point '$D$',which is at a vertical distance '$y_0$' below '$C$'. If the initial velocity of the ball is $15 \ m/s$,find $y_0$ (given $\cos 37^{\circ} = \frac{4}{5}$). (in $m$)