Question

A tank with vertical walls is mounted so that its base is at a height of $1.2m$ above the horizontal ground. The tank is filled with water to a depth $2.8m.$ A hole is punched in the side wall of thetank at a depth $xm$ below the surface of water to have maximum range of the emerging stream.Then the value of $x$ in meter is

• A. $4.0$
• B. $1.6$
• C. $2.0$
• D. $2.3$

Answer 1

The correct option is C $2.0$

Velocity of ejection at a depth x is $\sqrt{2gx}$
time of flight $=\sqrt{\frac{2H}{9}}=\sqrt{\frac{2(1.2+2.8-x)}{9}}$
$=\sqrt{\frac{2(4-x)}{9}}$
$\therefore$ Horizontal Range $R=Vt=\sqrt{4x(4-x)}$
$=2\sqrt{x(4-x)}$
$\frac{dR}{dx}=0\Rightarrow x=\frac{4}{2}=2m$