# Maximum height water can be projected onto a wall

• tycoon515
In summary, the problem is to determine the maximum height on a wall that a firefighter can project water from a hose with a speed of 20 m/s. The firefighter is 18 m away from the wall and holds the nozzle 1.2 m above the ground. The book solution suggests using the uniform acceleration kinematic equation to find the height as a function of launch angle and then maximizing it using calculus. However, the person who solved the problem used a different approach and got a different answer, which was determined to be correct.
tycoon515

## Homework Statement

H3-1 Determine the maximum height on the wall to which the firefighter can project water from the hose if the speed of the water at the nozzle is 20 m/s.
The firefighter stands 18 m away from the wall and holds the nozzle 1.2 m above the ground.

## The Attempt at a Solution

This is my work. What I did was solve for the time it took for the water to travel 18 m forward as a function of theta. Then I plugged this time into the uniform acceleration kinematic for vertical position to get height at the wall as a function of launch angle. I then maximized height using calculus and got an answer. My professor claims that my approach is not valid for this problem and suggests that the process shown in the attached solution sheet hw3s.pdf is the way to go. On the solution they start by saying that height is maximized when dy/dt = 0, so they assert that dy/dt at the wall must be zero. I'm skeptical of their approach. Here's my work:

#### Attachments

• hw3p.pdf
25.7 KB · Views: 434
• hw3s.pdf
23.9 KB · Views: 417
Hi Ty,

Can read the exercise and the book solution. Agree. Hard to read your writing, could you type it out ?

tycoon515, I agree with your answer. The max height on the wall does not correspond to the max height of the trajectory.

TSny read better than I. Once I turned your page over 90 degrees it became legible. Book answer is way wrong.
Hats off for your work !

## 1. How is the maximum height of water projected onto a wall determined?

The maximum height of water projected onto a wall is determined by several factors, including the initial velocity of the water, the angle at which it is projected, and the force of gravity. These factors can be calculated using mathematical equations to determine the maximum height the water can reach.

## 2. Can the maximum height of water projected onto a wall be higher than the initial velocity?

No, the maximum height of water projected onto a wall cannot be higher than the initial velocity. The initial velocity is the maximum speed at which the water is projected, and the force of gravity will always slow it down as it travels upwards, limiting the maximum height it can reach.

## 3. How does the viscosity of the water affect the maximum height it can be projected onto a wall?

The viscosity of water does not have a significant effect on the maximum height it can be projected onto a wall. Viscosity is the resistance of a fluid to flow, and while it may slightly affect the trajectory of the water, it will not have a significant impact on the maximum height it can reach.

## 4. Can the surface of the wall affect the maximum height of water projected onto it?

Yes, the surface of the wall can affect the maximum height of water projected onto it. A rough or uneven surface will cause the water to lose momentum and travel a shorter distance, resulting in a lower maximum height. A smooth surface will allow the water to maintain its velocity and reach a higher maximum height.

## 5. Is there a limit to the maximum height of water that can be projected onto a wall?

Yes, there is a limit to the maximum height of water that can be projected onto a wall. This limit is determined by the initial velocity, angle of projection, and force of gravity. Once these factors are calculated, the maximum height can be determined and there is no way to exceed it without changing one of these variables.

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