Question

Water drops are falling from a nozzle of a shower onto the floor, from a height of $9.8\text{m}$. The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of the second drop from the floor when the first drop strikes the floor.

• A. $2.45\text{m}$
• B. $7.35\text{m}$
• C. $2.94\text{m}$
• D. $4.18\text{m}$

Answer 1

The correct option is B $7.35\text{m}$

Time taken by the first drop to reach the ground is :

$t=\sqrt{\frac{2h}{g}}=\sqrt{2}\text{s}$

When the first drop reaches the ground, the third drop begins to fall. Therefore, the time interval between the drops is :

$\Delta t=\frac{t}{2}=\frac{1}{\sqrt{2}}$

Therefore, the distance covered by the second drop is :

$s=\frac{1}{2}g\Delta t^2$

$=\frac{1}{2}\times 9.8\times \frac{1}{2}=2.45\text{m}$

Therefore, the height of the second drop is :

$h=H-s=9.8-2.45=7.35\text{m}$

Hence, $\left(B\right)$ is the correct answer.