Drops of water fall at regular intervals from the roof of a building of height 16 m. The first drop strikes the ground at the same moment as the fifth drop leaves the roof. Find the distances between successive drops.

Explanation

Height of building , h= 16 m
`therefore` Time taken to reach the ground, `t=sqrt((2h)/g)`
`therefore` Time taken to fail, `t=sqrt((2times16)/9.8)`
`=sqrt(32/9.8)=sqrt3.26=1.80`
Number of drops ,n=5
`therefore` Number of intervals = n-1=5-1=4

Time interval between drops =`1.8/4`
=0.45 sec
Time of travel of 1st drop, `t_1=4 times 0.45=1.8`
`therefore` Distance travelled by
1st drop, `S_1=1/2g t _1^2=1/2times9.8times1.8times1.8=16m`
For 2nd drop, `t_2=3 times 0.45 =0.35 sec`.,
`S_2=1/2g t _2^2`,
`therefore S_2=1/2times9.8times1.35^2`
`=4.9 times1.822 =1.822=9m`
For 3rd drop , `t_3=2times.045=0.9 sec`.
Distance, `S_3=1/2g t _3^2=1/2times9.8times0.9^2=3.97`
=4 m
For 4th drop , `t_4=1times0.45=0.45sec`
Distance travelled, `S_4=1/2g t _4^2=1/2times9.8times(0.45)^2=1`
For 5 th drop, `t_5=0impliesS_5=0`
Distance between `1^(st)` and `2^(nd)` drop
`S_(1,2)=S_1-S_2=16-9=7m`
Distance between `2^(nd)` and `3^(rd)` drop
`S_(2,3)=S_2-S_3=9-4=5m`
Distance between `3^(rd)` and `4^(th)` drop
`S_(3,4)=S_3-S_4=4-1=3m`
Distance between `4^(th)` and `5^(th)` drop
`S_(4,5)=S_4-S_5=1-0=1m`
`therefore` Distances between successive drops are 7 m, 5 m, 3m and 1m.