An airplane is flying at a height of $490 \, m$ with a horizontal velocity of $60 \, km/h$. When the airplane is exactly above point $A$,a package is dropped from it. At what distance from point $A$ will the package hit the ground (in $/3 \, m$)? $(g = 9.8 \, m/s^2)$

$A$ fighter plane is flying horizontally at an altitude of $1.5\, km$ with a speed of $720\, km/h$. At what angle of sight (with respect to the horizontal) should the pilot drop the bomb when the target is seen,in order to hit the target?

Three balls,$A, B$ and $C$ are released and all reach the point $X$ (shown in the figure). Balls $A$ and $B$ are released from two identical structures,one kept on the ground and the other at height $h$ from the ground as shown in the figure. They take time $t_A$ and $t_B$ respectively to reach $X$ (time starts after they leave the end of the horizontal portion of the structure). The ball $C$ is released from a point at height $h$,vertically above $X$ and reaches $X$ in time $t_C$. Choose the correct option.

$A$ ball of mass $0.2 \ kg$ is thrown from a height of $1 \ m$ with an initial velocity of $\sqrt{10} \ m/s$ at an angle of $45^{\circ}$ with the horizontal. Assuming acceleration due to gravity $g = 10 \ m/s^2$,the modulus of the momentum increment during the total time of motion in $kg \cdot m/s$ is:

$A$ boy playing on the roof of a $10 \, m$ high building throws a ball with a speed of $10 \, m/s$ at an angle $30^{\circ}$ with the horizontal. How far from the throwing point will the ball be at the height of $10 \, m$ from the ground (in $, m$)? $(g = 10 \, m/s^2, \sin 30^{\circ} = 1/2, \cos 30^{\circ} = \sqrt{3}/2)$

$A$ gun can fire shells with maximum speed $v_0$ and the maximum horizontal range that can be achieved is $R = \frac{v_0^2}{g}$. If a target farther away by distance $\Delta x$ (beyond $R$) has to be hit with the same gun,show that it could be achieved by raising the gun to a height at least $h = \Delta x \left[ 1 + \frac{\Delta x}{R} \right]$.