Two projectiles are projected at $30^{\circ}$ and $60^{\circ}$ with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:

A ball is projected from ground with a velocity $V$ at an angle $\theta$ to the vertical. On its path it makes an elastic collison with a vertical wall and returns to ground. The total time of flight of the ball is 

A cart is moving horizontally along a straight line with a constant speed of $30\,m / s$. A projectile is to be fired from the moving cart in such a way that it will retum to the cart (at the same point on cart) after the cart has moved $80\,m$. At what velocity (relative to the cart) must be projectile be fired? (Take $=10\,m / s ^2$ )

A ball is projected at an angle $45^o$ with horizontal. It passes through a wall of height $h$  at horizontal distance $d_1$ from the point of projection and strikes the ground at a  horizontal distance $(d_1 + d_2)$ from the point of projection, then $h$ is

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

A projectile is fired from the surface of the earth with a velocity of  $5 \,m s^{-1}$ and angle $\theta$ with the horizontal. Another projectile fired from another planet with a velocity of $3 \,m s^{-1}$ at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in $\,m s^{-1}$) is 
(Given $g = 9.8 \,m s^{-2}$)