$A$ ball is thrown vertically upwards with a velocity of $19.6 \, m/s$ from the top of a tower. The ball strikes the ground after $6 \, s$. The height from the ground up to which the ball can rise is given by $\left(\frac{k}{5}\right) \, m$. The value of $k$ is ..... (use $g = 9.8 \, m/s^2$)

$A$ body thrown vertically upwards with an initial velocity $u$ reaches maximum height in $6$ seconds. The ratio of the distances travelled by the body in the first second and the seventh second is

$A, B, C$ are points in a vertical line such that $AB = BC$. If a body falls freely from rest at $A$,and $t_1$ and $t_2$ are the times taken to travel distances $AB$ and $BC$ respectively,then the ratio $(t_2 / t_1)$ is:

It is a common observation that rain clouds can be at about a kilometer altitude above the ground.
$(a)$ If a rain drop falls from such a height freely under gravity,what will be its speed? Also calculate in $km/h$ $(g = 10\, m/s^2)$.
$(b)$ $A$ typical rain drop is about $4\, mm$ in diameter. Momentum is mass $\times$ speed in magnitude. Estimate its momentum when it hits the ground.
$(c)$ Estimate the time required to flatten the drop.
$(d)$ Rate of change of momentum is force. Estimate how much force such a drop would exert on you.
$(e)$ Estimate the order of magnitude force on an umbrella. Typical lateral separation between two rain drops is $5\, cm$.
(Assume that the umbrella is circular and has a diameter of $1\, m$ and the cloth is not pierced through.)

$A$ stone is dropped into water from a bridge $44.1 \ m$ above the water. Another stone is thrown vertically downward $1 \ s$ later. Both strike the water simultaneously. What was the initial speed of the second stone in $m/s$?

$A$ body is projected vertically upward with a speed of $40 \, m/s$. The distance travelled by the body in the last second of its upward journey is ........... $m$. [Take $g = 9.8 \, m/s^2$ and neglect the effect of air resistance]