Free Fall Problem: Solve for Water Speed Leaving Nozzle

In summary, the question asks for the water speed as it leaves the nozzle when the nozzle is pointed vertically upward at a height of 1.5 meters above the ground and the water is heard striking the ground for 2.0 seconds after the nozzle is quickly moved away from the vertical position. By using the equation Xf = Xo + Vot + (1/2)at2 and solving for the initial velocity Vo, the water speed is calculated to be 9.1 m/s. The problem was classified as 'hard' and typically requires multiple steps to solve, but the answer was obtained in one step.
  • #1
Quincy
228
0

Homework Statement


Suppose you adjust your garden hose nozzle for a hard stream of water. You point the nozzle vertically upward at a height of 1.5 meters above the ground. When you quickly move the nozzle away from the vertical, you hear the water striking the ground next to you for another 2.0 seconds. What is the water speed as it leaves the nozzle?


Homework Equations


Xf = Xo + Vot + (1/2)at2


The Attempt at a Solution



Xf = Xo + Vot + (1/2)at2
-1.5 m = Vo(2) + (1/2)(-9.8)(4)
Vo = 9.1 m/s
 
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  • #2
That looks right. Is there a question?
 
  • #3
Looks good.
 
  • #4
The difficulty level for this problem was 'hard.' Most of these problems take at least 3 steps to solve. I thought I did something wrong since I got the answer in one step...
 

FAQ: Free Fall Problem: Solve for Water Speed Leaving Nozzle

What is free fall and how does it relate to water speed?

Free fall is the motion of an object under the influence of gravity alone, without any external forces acting upon it. In the context of water speed, free fall refers to the downward motion of water as it exits a nozzle due to the force of gravity.

How is the speed of water leaving a nozzle calculated in a free fall problem?

The speed of water leaving a nozzle in a free fall problem can be calculated using the equation v = √(2gh), where v is the speed of the water, g is the acceleration due to gravity (9.8 m/s²), and h is the height of the nozzle above the ground.

Can air resistance affect the speed of water in a free fall problem?

In most cases, air resistance is negligible when it comes to the speed of water in a free fall problem. This is because air resistance only becomes significant at high speeds, and the speed of water leaving a nozzle is relatively low compared to other free fall scenarios.

How does the shape and size of the nozzle affect the speed of water in a free fall problem?

The shape and size of the nozzle can affect the speed of water in a free fall problem. A narrower nozzle will result in a higher velocity of water due to the Venturi effect, while a wider nozzle will result in a lower velocity. Additionally, the shape of the nozzle can also impact the direction of the water's motion.

What are some real-world applications of free fall problems involving water speed?

Some real-world applications of free fall problems involving water speed include determining the speed of water exiting a fountain or a water slide, calculating the flow rate of a waterfall, and designing irrigation systems for agriculture. Free fall problems involving water speed are also important in fluid mechanics and engineering.

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