Question

An open tank of height H is completely filled and is kept on a table of height 2H. At what height from the ground, a small hole should be made in the wall of the tank, so that the range on ground becomes maximum?​

Answer 1

Answer:

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Answer 2

A small hole should be made in the tank at 1.5 H

To find:

Where a small hole should be made in the tank.

Given:

Height of tank = H

Height of the table = 2H

Solution:

Let required height from ground = h

V_e = √(2g(3H-h))

Where g is the acceleration due to gravity.

For vertical motion,

H= ½ gt^2

T= √(2h/g)

X= V_e *t = √(2g(3H-h)) * √(2h/g)

X= 2√(h(3H-h))

For maximum X

dX/dh = 0

d/dh (2√(h(3H-h))) = 0

3H-h-h = 0

h= 3H/2 =1.5H

Because this point is in the tank, the hole should be made at this point.

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