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Question

Raindrops fall $$1700\, m$$ from a cloud to the ground. If they were not slowed by air resistance, how fast would the drops be moving when they hit the ground?

Solution
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Given:
$$s = 1700\,m$$ (taking downward direction positive)

Then, if the raindrops start from rest, $$u=0$$,
Using $$3^{rd}$$ law of motion
$$2 as=v^2 - u^2$$
$$ 2 \times (9.8)\times (1700) = v^2 -u^2$$
$$ 33320 = v^2 -(0)^2$$
$$\Rightarrow v= \sqrt{33320}$$
$$\Rightarrow v= 182.54\,m/s$$

Thus the drops are moving with a velocity of $$182.54\,m/s$$ in downward direction.

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