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Water drips from a leaky rainspout that is located at the top of a high building. The droplets of water fall at an interval of 1/2 second. As time passes, the distance between two consecutive drops of water (A) decreases in a linear manner. (B) increases in a linear manner. (C) remains the same. (D) decreases in a parabolic manner. (E) increases in a parabolic manner. Please provide the answer with explanation

Water drips from a leaky rainspout that is
located at the top of a high building. The
droplets of water fall at an interval of 1/2
second. As time passes, the distance between
two consecutive drops of water
(A) decreases in a linear manner.
(B) increases in a linear manner.
(C) remains the same.
(D) decreases in a parabolic manner.
(E) increases in a parabolic manner.
 
Please provide the answer with explanation

Grade:12

1 Answers

Shobhit Varshney IIT Roorkee
askIITians Faculty 33 Points
6 years ago
Hi,

Assume at t=0, first drop starts to fall.
So, its distance from the rainspout, h1= 0.5 g t2

At t = 0.5 s, next drop starts to fall.
So, its distance from the rainspout, h2= 0.5 g (t – 0.5)2

Separation between them at any time t = h1–h2
= 0.5 g [t2– (t – 0.5)2]
= 0.25 g (2t – 0.5)

So, it increases in a linear manner.

thanks

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