Question

The water level is maintained in a cylindrical vessel up to a fixed height H. The vessel is kept on a horizontal plane. At what height above the bottom should a hole be made in the vessel so that the water stream coming out of the hole strikes the horizontal plane at the greatest distance from the vessel

Answer 1

The question is asked about the range.

I means to say that, when water is flowing out from the orifice, then it will fall on earth. The motion of its fall will be projectile. Now, we need to find the height of the orifice to be as such so that the Range is maximum.

Now, Listen!,

Range is given by the formula,

 $R = \sqrt{4h(H - h)}$

where, H is the height of the cylindrical vessel, h is the height of the orifice and R is the Range.

Now, R will be maximum when R² is maximum.

Let us find the maximum value of R², which will also give the value of R when it will be maximum.

∴  dR²/dh = 0

 $\frac{d(h(H-h))}{dh} = 0$

d(Hh)/dh - d(h)²/dh = 0

H × 1 = 2h

h = H/2.

When the orifice will be at the centre of its height, then the range will be maximum.

Hope it helps.

Answer 2

Answer:

hope it is helpful....

please mark it as brainliest.....