Question

From a tap $10m$ high, water drops fall at regular intervals. When the first drop reaches the ground, the $5^{th}$ drop is about to leave the tap. Find the separation between $2^{nd}$ and $3^{rd}$ drops.

• A. $\frac{35}{8}m$
• B. $\frac{31}{8}m$
• C. $\frac{27}{8}m$
• D. $\frac{25}{8}m$

Answer 1

The correct option is D $\frac{25}{8}m$

From the given situation,
$\frac{1}{2}g{t}^2=10$
$t=\sqrt{2}s$

Time interval
$\Delta t=\frac{\sqrt{2}}{4}=\frac{1}{2\sqrt{2}}s$
Now, $x_2-x_3=\frac{1}{2}g[{\left(\frac{3}{2\sqrt{2}}\right)}^2-{\left(\frac{2}{2\sqrt{2}}\right)}^2]$
$x_2-x_3=\frac{25}{8}m$