A cylindrical vessel is filled with water to a height H . A...

A cylindrical vessel is filled with water to a height $H . A$ vessel has two small holes in the side, from which water is rushing out horizontally and the two streams strike the ground at the same point. If the lower hole $Q$ is $h$ height above the ground, then the height of hole $P$ above the ground will be: (a) $2 h$ (b) $\mathrm{H} / \mathrm{h}$ (c) $H-h$ (d) $\mathrm{H} / 2$

A cylindrical vessel is filled with water to a height $H . A$ vessel has two small holes in the side, from which water is rushing out horizontally and the two streams strike the ground at the same point. If the lower hole $Q$ is $h$ height above the ground, then the height of hole $P$ above the ground will be:
(a) $2 h$
(b) $\mathrm{H} / \mathrm{h}$
(c) $H-h$
(d) $\mathrm{H} / 2$

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Key Concepts

Torricelli's Law

This law states that the speed at which a fluid exits an orifice under gravity is proportional to the square root of the vertical distance between the fluid surface and the orifice. It is crucial for determining the initial velocity of the water stream as it leaves the vessel.

Horizontal Projectile Motion

In horizontal projectile motion, an object launched with an initial horizontal velocity has its vertical displacement governed solely by gravity. The time to fall to the ground depends only on the height from which it is projected, while the horizontal distance traveled is the product of the constant horizontal speed and the time of flight.

Combining Fluid Dynamics with Projectile Motion

This concept involves using both Torricelli's law and the principles of projectile motion to analyze the trajectory of a water jet. By equating the horizontal distances traveled by streams exiting the vessel at different heights, one can deduce relationships between the positions of the orifices relative to the ground.

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