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# Drops are falling at regular intervals of time from the roof of a building 16 m high. If the first drop reaches the ground at the instant the fifth drop start falling, find the heights of the various drops at the instant the first drop reaches the ground ?

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Let the drops fall at a regular interval of time t.
When the fifth drop starts falling, the time elapsed will be $t,2t,3t$ and $4t$ for the fourth , third, second and first drop respectively and if the distances covered are $S_4,S_3,S_2,S_1$ then
$S_1= \large\frac{1}{2}$$g(4t)^2=16 \times \large\frac{1}{2}$$gt^2$
$S_2= \large\frac{1}{2}$$g(3t)^2=9 \times \large\frac{1}{2}$$gt^2$
$S_3= \large\frac{1}{2}$$g(2t)^2=4 \times \large\frac{1}{2}$$gt^2$
$S_4= \large\frac{1}{2}$$g(t)^2= \large\frac{1}{2}$$gt^2$
Here $S_1= 16 m$ Therefore $\large\frac{1}{2}$$gt^2=1m$
Hence $S_2= 9 m,S_3= 4 m$ and $S_1 =1m$ .
The height of the various drops from the surface of the earth will be $0,7,12,15\;and \;16 m$
answered Jul 25, 2014 by