$A$ body falls from rest in the gravitational field of the earth. The distance travelled in the fifth second of its motion is ......... $m$ $(g = 10\,m/s^2)$.

$A$ ball is dropped from a height of $90 \; m$ on a floor. At each collision with the floor,the ball loses one-tenth of its speed. Plot the speed-time graph of its motion between $t = 0$ to $12 \; s$.

$A$ body is thrown vertically upwards. If air resistance is to be taken into account,then the time during which the body rises 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 thrown upward with a speed $u$ from the top of a tower reaches the ground with a velocity $3u$. The height of the tower is (in $u^2/g$)

$A$ stone falls freely such that the distance covered by it in the last second of its motion is equal to the distance covered by it in the first $5 \,s$. It is in air for....... $s$.