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 $4 \,mm$ diameter. Momentum is mass $\times $ speed in magnitude. Estimate its momentum when it hits 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 umbrella. Typical lateral separation between two rain drops is $5\, cm$.

(Assume that umbrella is circular and has a diameter of $1\, m$ and cloth is not pierced through.)

A body is thrown vertically upwards and takes $5$ seconds to reach maximum height. The distance travelled by the body will be same in

A stone is dropped from a height $h$. Simultaneously, another stone is thrown up from the ground which reaches a height $4 \,h$. The two stones cross each other after time

A ball is thrown vertically upwards with a veloctty of $20 \;\mathrm{m} \mathrm{s}^{-1}$ from the top of a multistorey building. The helght of the point from where the ball is thrown is $25.0\; \mathrm{m}$ from the ground. how long will it be in $seconds$ before the ball hits the ground? Take $g=10 \;\mathrm{m} \mathrm{s}^{-2}$

A body starts to fall freely under gravity. The distances covered by it in first, second and third second are in ratio