Drops-are-falling-regularly-from-a-water-tap-at-a-height-of-9-m-from-the-ground-The-4-th-drop-is-about-to-fall-from-the-tap-when-the-1-st-hit-the-ground-Find-the-distance-between-2-nd-and-3

Question Number 15115 by Tinkutara last updated on 07/Jun/17

Drops are falling regularly from a water

tap at a height of 9 m from the ground .

The 4^{th} drop is about to fall from the

tap when the 1^{st} hit the ground . Find

the distance between 2^{nd} and 3^{rd} drop .

Answered by mrW1 last updated on 07/Jun/17

9 = \frac{1}{2} \times 10 \times t^{2}

\Rightarrow t = \sqrt{1.8} s

Δ t = \frac{t}{3} = \sqrt{0.2} s

Δ h_{2 - 3} = \frac{1}{2} \times 10 \times [{(2 Δ t)}^{2} - Δ t^{2}]

= \frac{1}{2} \times 10 \times 3 \times 0.2 = 3 m

or :

H_{1} = \frac{1}{2} g {(3 t)}^{2}

H_{2} = \frac{1}{2} g {(2 t)}^{2}

H_{3} = \frac{1}{2} g {(t)}^{2}

H_{4} = 0

Δ H_{2 - 3} = \frac{1}{2} g ({4 t}^{2} - t^{2}) = \frac{3}{2} {gt}^{2} = \frac{1}{3} \times \frac{1}{2} g {(3 t)}^{2}

= \frac{1}{3} H_{1} = \frac{9}{3} = 3 m

Commented by Tinkutara last updated on 07/Jun/17

Thanks Sir!