Question

Drops of water falls from the roof of a building $9$m high at regular intervals of time, the first drop reaching the ground at the same instant fourth drop starts to fall. What are the distances of the second and third drops from the roof.

• A. $6m$ and $2m$
• B. $6m$ and $3m$
• C. $4m$ and $1m$
• D. $4m$ and $2m$

Answer 1

Answer: (C)

$4m$ and $1m$

Let the time interval between falling two drops from the roof be t seconds.

Then $4th$ drop falls after $3t$ seconds of falling of first drop

$\therefore$ The time of flight of $1st$ drop

$=3t$sec

$H=\frac{1}{2}g{t}^2$

$9=\frac{1}{2}g9t^2$

$\frac{18}{g}=9t^2;t=\sqrt{\frac{2}{g}}$

$t=\sqrt{\frac{2}{10}}=\sqrt{\frac{1}{5}}$

Distance of $2nd$ drop from the roof

$H=\frac{1}{2}g\frac{1}{5}=1m$ or $H=\frac{1}{2}g{\left(t\right)}^2$

Distance of $3rd$ drop from the roof

$H=\frac{1}{2}g\frac{4}{5}$ or $H=\frac{1}{2}g{\left(2t\right)}^2$

$=4m$