$A$ ball is thrown upward from the top of a building at an angle of $30^{\circ}$ to the horizontal and with an initial speed of $20 \,m/s$. If the ball strikes the ground after $3 \,s$, then the height of the building is (acceleration due to gravity $g = 10 \,m/s^2$) (in $\,m$)

$A$ helicopter flying horizontally with a speed of $360 \ km/h$ at an altitude of $2 \ km$,drops an object at an instant. The object hits the ground at a point $O$,$20 \ s$ after it is dropped. The displacement of $O$ from the position of the helicopter where the object was released is: (use acceleration due to gravity $g = 10 \ m/s^2$ and neglect air resistance)

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?

An aeroplane moving horizontally with a speed of $720 \, km/h$ drops a food packet while flying at a height of $396.9 \, m$. The time taken by the food packet to reach the ground and its horizontal range are (Take $g = 9.8 \, m/s^2$):

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 $90^o$?

$A$ cannon ball is fired from the top of a $55 \ m$ high cliff with an initial speed of $50 \ m \ s^{-1}$. The speed of the cannon ball while hitting the ground in $m \ s^{-1}$ is (acceleration due to gravity $= 10 \ m \ s^{-2}$):