$A$ 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 $= 10 \ m \ s^{-2}$):

Projectiles $A$ and $B$ are thrown at angles of $45^{\circ}$ and $60^{\circ}$ with the vertical,respectively,from the top of a $400 \ m$ high tower. If their ranges and times of flight are the same,the ratio of their speeds of projection $v_A : v_B$ is:

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 $g = 10 \text{ m/s}^2$)

$A$ 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:

$A$ body is projected horizontally from a height with a speed of $20 \, m/s$. What will be its speed after $5 \, s$ (in $, m/s$)? (Take $g = 10 \, m/s^2$)

$A$ stone is projected at an angle of $60^o$ from the ground level and strikes at an angle of $30^o$ on the roof of a building of height $h = 30 \, m$. Find the speed of projection (in $m/s$) of the stone.