Q: Drops of water fall from the root of a building 9 m high at regular intervals of time, the first drop reaching the ground at the same instant fourth drop starts its fall. What are the distances of the second and third drops from the roof ? (g = 10 ms )

(a) 6 m and 2 m

(b) 6 m and 3 m

(c) 4 m and 1 m

(d) 4 m and 2 m

Ans:(c)

Sol: Time taken by first drop to reach the ground

$\displaystyle t = \sqrt{\frac{2 h}{g}}$

$ \displaystyle t = \sqrt{\frac{2 \times 9}{10}}$

t = 1.36 sec

Time interval between successive drops

= 1.36/3 sec

Applying ,

$ \displaystyle S = u t + \frac{1}{2}a t^2 $

Distance of 2rd drop,

$ \displaystyle S_2 = 0 + \frac{1}{2}(10) (\frac{2}{3}\times 1.36)^2 $

S_{2} = 4 m

Distance of 3rd drop,

$ \displaystyle S_3 = 0 + \frac{1}{2}(10) (\frac{1}{3}\times 1.36)^2 $

S_{3} = 1 m