Question

You're holding a hose at waist height and spraying water horizontally with it. The hose nozzle has a diameter of 1.80 $\mathrm{cm},$ and the water splashes on the ground a distance of 0.950 m horizontally from the nozzle. Suppose you now constrict the nozzle to a diameter of 0.750 $\mathrm{cm}$ ; how far horizontally from the nozzle will the water travel before hitting the ground? (Ignore air resistance.)

Name: Problem 46, Chapter 13: College Physics
Uploaded: 2019-05-26T23:49:18-08:00
Duration: 2 min 23 s
Channel: Elan Stopnitzky
Description: You're holding a hose at waist height and spraying water horizontally with it. The hose nozzle has a diameter of 1.80 cm, and the water splashes on the ground a distance of 0.950 m horizontally from the nozzle. Suppose you now constrict the nozzle to a diameter of 0.750 cm ; how far horizontally from the nozzle will the water travel before hitting the ground? (Ignore air resistance.)

   You're holding a hose at waist height and spraying water horizontally with it. The hose nozzle has a diameter of 1.80 $\mathrm{cm},$ and the water splashes on the ground a distance of 0.950 m horizontally from the nozzle. Suppose you now constrict the nozzle to a diameter of 0.750 $\mathrm{cm}$ ; how far horizontally from the nozzle will the water travel before hitting the ground? (Ignore air resistance.)

College Physics

Hugh D. Young 9th Edition

Chapter 13, Problem 46

Instant Answer

Solved by Expert Elan Stopnitzky

05/26/2019

Step 1

The radius of the hose is half of its diameter. So, the initial radius $r_1$ is $\frac{1.80}{2} \times 10^{-2} = 0.009 \, \mathrm{m}$ and the final radius $r_2$ is $\frac{0.75}{2} \times 10^{-2} = 0.00375 \, \mathrm{m}$. Show more…

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You're holding a hose at waist height and spraying water horizontally with it. The hose nozzle has a diameter of 1.80 $\mathrm{cm},$ and the water splashes on the ground a distance of 0.950 m horizontally from the nozzle. Suppose you now constrict the nozzle to a diameter of 0.750 $\mathrm{cm}$ ; how far horizontally from the nozzle will the water travel before hitting the ground? (Ignore air resistance.)

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Key Concepts

Projectile Motion

This concept explains that when an object (or water jet) is projected horizontally, its vertical motion is governed solely by gravity, while its horizontal motion continues at a constant speed (if air resistance is ignored). The time it takes for the water to hit the ground depends only on the vertical distance and the acceleration due to gravity, and the horizontal distance (range) is the product of this time and the initial horizontal speed.

Continuity Equation

In fluid dynamics, the continuity equation expresses the conservation of mass for an incompressible fluid. It relates the fluid’s velocity to the cross-sectional area of the flow; when the area decreases (as when a nozzle is constricted), the velocity must increase proportionally to maintain a constant flow rate. This relationship is crucial for understanding how a change in the nozzle diameter affects the water's exit speed and ultimately its horizontal range when projected.

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