$A$ bomb is released from a horizontal flying aeroplane. The trajectory of the bomb 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 return to the cart (at the same point on the cart) after the cart has moved $80\,m$. At what velocity (relative to the cart) must the projectile be fired? (Take $g = 10\,m/s^2$)

$A$ stone is projected from the ground with velocity $50 \, m/s$ at an angle of $30^o$. It crosses a wall after $3 \, s$. How far beyond the wall will the stone strike the ground? $(g = 10 \, m/s^2)$

An object is projected from the ground with speed $u$ at an angle $\theta$ with the horizontal. The radius of curvature of its trajectory at the maximum height from the ground is ..........

$A$ body is projected from the ground at an angle of $\tan^{-1}(\sqrt{7})$ with the horizontal. At half of the maximum height, the speed of the body is '$n$' times the speed of projection. The value of '$n$' is

$A$ stone is thrown vertically at a speed of $30 \,ms^{-1}$ making an angle of $45^{\circ}$ with the horizontal. What is the maximum height reached by the stone (in $\,m$)? Take $g=10 \,ms^{-2}$.