Question

1.
A cylindrical vessel is filled with water up to height H. A hole
is bored in the wall at a depth h from the free surface of water.
For maximum range, h is equal to
H
3H
(c) -
(a) H
(b)
(c) 38
(d) H​

Answer 1

Answer:

Maximum range of the water from the hole is R = H

Explanation:

Let the hole is bored at distance y from free surface of the water

So here the speed of water by which it eject out from the bore is given as

$v = \sqrt{2gy}$

now height from the ground of the hole is given as

$h = H - y$

time taken by the water to hit the ground is given as

$t = \sqrt{\frac{2(H - y)}{g}}$

so the range of the water is given as

$R = v_x \times t$

$R = \sqrt{2gy}\times \sqrt{\frac{2(H - y)}{g}}$

so we have

$R = 2\sqrt{y(H - y)}$

now for maximum range we have

$\frac{dR}{dy} = 0$

so we get

$y = \frac{H}{2}$

Now maximum range is given as

$R = H$

#Learn

Topic : Flow of water from the hole

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