Two balls are thrown horizontally from the top of a tower with velocities $v_1$ and $v_2$ in opposite directions at the same time. After how much time will the angle between the velocities of the balls become $90^o$?

An archer shoots an arrow from a height of $4.2 \text{ m}$ above the ground with a speed of $40 \text{ m/s}$ at an angle of $30^{\circ}$ with the horizontal, as shown in the figure. Determine the total horizontal distance $R$ covered by the arrow when it hits the ground. (Take $g = 10 \text{ m/s}^2$)

An aeroplane is moving with horizontal velocity $u$ at height $h$. The velocity of a packet dropped from it on the earth's surface will be ($g$ is acceleration due to gravity).

$A$ body is projected horizontally with a velocity of $4\,m/s$ from the top of a high tower. The velocity of the body after $0.7\,s$ is nearly $.....\,m/s$ (take $g=10\,m/s^2$).

Two particles in the same vertical plane are thrown to strike at the same time. One is thrown from the ground and the other from a height $h$ vertically above it. The ground particle is thrown obliquely with speed $u$ at an angle $\theta$ and achieves a maximum height $H$. The second particle is thrown horizontally with the same speed $u$. What is the maximum height $h$ such that the two particles strike each other in the air?

$A$ cannon placed on a cliff at a height of $375 \ m$ fires a cannonball with a velocity of $100 \ ms^{-1}$ at an angle of $30^{\circ}$ above the horizontal. The horizontal distance between the cannon and the target is (Acceleration due to gravity $= 10 \ ms^{-2}$)