Question

Water stands at a depth ‘H’ in a tank whose side walls are vertical. If a hole is made on one of the walls at a depth ‘h’ below the water surface, then find
i. At what distance from the foot of the wall does the emerging stream of water strike the floor?
ii. What value of h this range is maximum?

Answer 1

We know that Va=√2gh ---------------------(1)

(H-h)=(1/2) gt² --------------------(2)

The distance R,
R=Vax T ----------------------------(3) [ Speed = Distance /time]
From equation (2) we get 

t=√2(H-h)/g -------------------(4)

Substituting the value of Va from equation I and the value of t from equation [iv] in  equation [iii] we get ,

R=√2gh  x √ 2(H-h)/g

R=2√ h(H-h)

The range will be at maximum when dR/dh =0

Answer 2

We know that Va=√2gh ---------------------(1)

(H-h)=(1/2) gt² --------------------(2)

The distance R,

R=Vax T ----------------------------(3) [ Speed = Distance /time]

From equation (2) we get

t=√2(H-h)/g -------------------(4)

Substituting the value of Va from equation I and the value of t from equation [iv] in equation [iii] we get ,

R=√2gh x √ 2(H-h)/g

R=2√ h(H-h)

The range will be at maximum when dR/dh =0