It is a common observation that rain clouds can be at about a kilometre altitude above the ground.a) If a raindrop falls from such a height freely under gravity, what will be its speed? Also, calculate in km/hb) A typical raindrop is about 4 mm diameter. Momentum is mass x 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 raindrops is 5 cm.

Thus,

(a) Let's find out the velocity of raindrop on the ground’

$\\v^{2}=u^{2}-2as\\=u^{2}-2g(-h)\\=u^{2}+2gh\\=0^{2}+2(10)(1000)$

Thus,

$\\v=100\sqrt{2}\; m/s\\v=100\sqrt{2}\left ( \frac{18}{5} \right )km/hr$

(b) Momentum of the raindrop when it touches the ground

mass of drop(m) = Vol. × density

Now, density of water

Thus,

Now, we know that Momentum (p) = mv

(c) Time required for a drop to be flattened-

(d) Now, we know that,

(e) Here,

Thus, Area of umbrella

Now, the square area covered by one drop

$= (5 \times 10^{-2})^{2}$

Therefore, no. of drops falling on the umbrella

Therefore 314 drops fell on the umbrella.

Thus, the net force on the umbrella