Question

Drops of water falls from the roof of a building $18m$ high in regular intervals of time. When the first drop reaching the ground, at the same instant fourth drop starts to fall. What are the distance of the second and third drops from the roof?

• A. $6m$ and $2m$
• B. $6m$ and $3m$
• C. $8m$ and $2m$
• D. $4m$ and $2m$

Answer 1

The correct option is C $8m$ and $2m$

Let interval of fall $=t$ (for the first drop ${}^{\prime }{t}^{\prime }=3t$)
$\therefore 3t=\sqrt{\frac{2\times 9}{10}}\Rightarrow t=\frac{1}{\sqrt{5}}$
For $2^{nd}$ drop $s_2=\frac{1}{2}\times 10\times \left(2t\right)=5\times 4\times \frac{1}{5}=4m$
for $3^{rd}$ drop $s_3=\frac{1}{2}g{t}^2=\frac{1}{2}\times 10\times \frac{1}{5}=1m$