The water surface in a large open tank is 12 m above horizontal ground. A small hole may be made anywhere in the vertical wall. Neglecting viscosity, at what height above the ground should the hole be made so that the water jet has maximum horizontal range before striking the ground?
Options

Question

The water surface in a large open tank is 12 m above horizontal ground. A small hole may be made anywhere in the vertical wall. Neglecting viscosity, at what height above the ground should the hole be made so that the water jet has maximum horizontal range before striking the ground?

Options

G1 Physics · Accepted Answer

Let the hole be at height y above the ground. The depth of the hole below the water surface is h = 12−y. Efflux speed is v = √[2g(12−y)]. The time taken by the jet to fall from the hole to the ground is t = √(2y/g). Therefore the horizontal range is R = vt = √[2g(12−y)] × √(2y/g) = 2√[y(12−y)]. For fixed total height 12 m, the product y(12−y) is maximum when y = 12/2 = 6 m. Correct option: C.