Question

Water drips from a faucet at a uniform rate of m drops per second. Find the distance x between the two adjacent drops as a function of time t that the

Answer 1

distance between two adjacent drops as function of time t is x = gt/m + g/2m²

Let first water drop in time t sec .

distance travelled first drop, x1 = 1/2 gt²

here water drops from a faucet at a uniform rate m drops /sec.

⇒m drops take 1 sec , so 1 drop takes 1/m sec

as 2nd drop is 1/m sec ahead from previous (1st ) one.

so, distance travelled by 2nd drop, x2 = 1/2 g(t + 1/m)²

now distance between two adjacent drops , x = x2 - x1

= 1/2 g(t + 1/m)² - 1/2gt²

= 1/2 g [ t² + 1/m² + 2t/m - t²]

= 1/2 g/m² + gt/m

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Answer 2

$\huge\bold\purple{Answer:-}$

Let first water drop in time t sec .

distance travelled first drop, x1 = 1/2 gt²

here water drops from a faucet at a uniform rate m drops /sec.

⇒m drops take 1 sec , so 1 drop takes 1/m sec

as 2nd drop is 1/m sec ahead from previous (1st ) one.

so, distance travelled by 2nd drop, x2 = 1/2 g(t + 1/m)²

now distance between two adjacent drops , x = x2 - x1

= 1/2 g(t + 1/m)² - 1/2gt²

= 1/2 g [ t² + 1/m² + 2t/m - t²]

= 1/2 g/m² + gt/m