Question

A water tank is filled with water upto height H. A hole is made in a tank wall at a depth D from the surface of water. The distance X from the lower end of wall where the water stream from tank strikes the ground is:

• A. $2\sqrt{gD}$
• B. $2\sqrt{D(H+D)}$
• C. $2\sqrt{D(H-D)}$
• D. $\sqrt{D}$

Answer 1

The correct option is C $2\sqrt{D(H-D)}$

Velocity of efflux at point D = $\sqrt{2gD}$
Time taken to reach the ground = $\sqrt{\frac{2(H-D)}{g}}$
So horizontal range = velocity $\times$ time = $\sqrt{2gD}\times \sqrt{\frac{2(H-D)}{g}}$
So range of the water stream $X=2\sqrt{D(H-D)}$