A hole is punched at a height h in the side of a container...

A hole is punched at a height $h$ in the side of a container of height $h_{0}$. The container is full of water, as shown in Figure $\mathrm{P} 15.45$. If the water is to shoot as far as possible horizontally, (a) how far from the bottom of the container should the hole be punched? (b) Neglecting frictional losses, how far (initially) from the side of the container will the water land?

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Key Concepts

Projectile Motion

Projectile motion examines the behavior of an object being thrown or projected, moving under the influence of gravity. It involves concepts such as time of flight, horizontal displacement, and vertical drop, and it is essential for understanding how a water jet travels once it exits a container through a hole.

Torricelli’s Law

Torricelli’s Law relates the speed at which a fluid exits an orifice to the height of the fluid above the opening. It states that the exit velocity is proportional to the square root of the product of gravitational acceleration and the vertical distance from the fluid surface to the hole, which in this case determines the initial velocity of the water jet.

Optimization

Optimization in the context of projectile motion involves determining the conditions that maximize a given outcome, such as the horizontal distance the water travels. It requires setting up an equation for the range and finding its maximum value, which leads to the conclusion that there is an optimal location on the container's side for punching the hole.

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