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Drops of water fall at regular intervals...

Drops of water fall at regular intervals from the roof of a building of height `h=16m`. The first drop striking the ground at the same moment as the fifth drop is ready to leave from the roof. Find the distance between the successive drops.

Text Solution

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Step -I Time taken by the first drop to touch the ground ` = t = sqrt((2h)/(g))`
For h = 16m, `t = sqrt((16(2))/(g))=4sqrt((2)/(g))`
Time interval between two successive drop is
`Deltat = ((1)/(n-1)) t = ((1)/(4))t = sqrt((2)/(g))`
Where n = number of drops
Step-II : Distance travelled by 1st drop
`S_(1) = (1)/(2)g (4Deltat)^(2) = (1)/(2)g(16)((2)/(g)) = 16m`
Distance travelled by 2nd drop
`S_(2) = (1)/(2)g(3Deltat)^(2) = (1)/(2)g(9)((2)/(9)) = 9m`
Distance travelled by 3rd drop
`S_(3) = (1)/(2)g(2Deltat)^(2) = (1)/(2)g((2)/(g)) = 1m`
Distance between 1st and 2nd drops =
`S_(1) - S_(2) = 16-9 = 7m`
Distance between 2nd and 3rd drops =
` S_(2) - S_(3) = 9 - 4 = 5m`
Distance between 3rd and 4th drops =
`S_(3) = S_(4) = 4 - 1 = 3m`
Distance between 4th and 5th drops =
`S_(4) - S_(5) = 1 - 0 = 1 m`
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