Question

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♦Water droplets of falling from a tap 5 metre above the ground at regular time intervals. 1st drop touches the ground when 5th is about to leave. find the height of the 3rd drop from the ground...?
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Answer 1

Answer:

Water droplets of falling from a tap 5 metre above the ground at regular time intervals. 1st drop touches the ground when 5th is about to leave. find the height of the 3rd drop from the ground is 3.75 meter

Explanation:

For the first droplet, apply

$s \: = \: ut \: + \: (1 \div 2) \: a{t}^{2}$

5 = 0 + 1/2gt^2

t^2=10/g

t=√(10/g)

This is the time interval required for 1st droplet to fall

After this time interval the fifth droplet is just about to leave

As the droplets fall at equal intervals, therefore

Time interval difference between two consecutive droplets is

T= t/4 = √(10/g)/4 = √(10/16g) = √(5/(8g)) ----(1)

Therefore Time required for Third droplet to touch ground is 2T = 2√(5/(8g)) = √(5/(2g)) -----(2)

The velocity of the third droplet when the first droplet is about to touch the ground is

V = u + at

V = 0 + g(2T)

V = 2gT

from (1)

V = √(5/(2g))g

V = √(5g/2) ------(3)

Therefore the distance of the Third droplet from the ground is

$s \: = ut \: + \: (1 \div 2)a {t}^{2}$

from (2) & (3)

S = √(5g/2)*√(5/(2g)) + (1/2)*g*(√(5/(2g)))^2

S=5/2+ (1/2)*g*(5/(2g))

S = 5/2 + 5/4

S = (10+5)/4

S = 15/4

S = 3.75 m

Answer 2

Refer the attachment.. ⭐

Hope it helps you..⭐