**Problem Statement: Calculating Power for a Fire Hose Water Pump**A fire engine must lift 30 kg of water a vertical distance of 20 meters each second. What is the amount of power needed for the water pump for this fire hose?**Solution Explanation:**1. **Force Calculation**: To lift the water, the fire engine must overcome gravitational force. Therefore, the force (F) required can be calculated using the formula: \[ F = m \times g \] where: - $ m = 30 \, \text{kg} $ is the mass of the water. - $ g = 9.81 \, \text{m/s}^2 $ is the acceleration due to gravity.2. **Work Calculation**: Work (W) done to lift the water can be calculated using: \[ W = F \times d \] where: - $ d = 20 \, \text{m} $ is the vertical distance the water is lifted.3. **Power Calculation**: Since power (P) is the work done per unit time (t), and here the time is one second, we can calculate power as: \[ P = \frac{W}{t} \] **Note**: This is a simplified model assuming no energy loss due to friction or air resistance.

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Description: **Problem Statement: Calculating Power for a Fire Hose Water Pump**A fire engine must lift 30 kg of water a vertical distance of 20 meters each second. What is the amount of power needed for the water pump for this fire hose?**Solution Explanation:*

Mass is In one second , the vertical distance covered is Note:Gravitational acceleration is…

Answered: A fire engine must lift 30 kg of water…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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**Problem Statement: Calculating Power for a Fire Hose Water Pump**

A fire engine must lift 30 kg of water a vertical distance of 20 meters each second. What is the amount of power needed for the water pump for this fire hose?

**Solution Explanation:**
1. **Force Calculation**:
To lift the water, the fire engine must overcome gravitational force. Therefore, the force (F) required can be calculated using the formula:
\[ F = m \times g \]
where:
- $ m = 30 \, \text{kg} $ is the mass of the water.
- $ g = 9.81 \, \text{m/s}^2 $ is the acceleration due to gravity.

2. **Work Calculation**:
Work (W) done to lift the water can be calculated using:
\[ W = F \times d \]
where:
- $ d = 20 \, \text{m} $ is the vertical distance the water is lifted.

3. **Power Calculation**:
Since power (P) is the work done per unit time (t), and here the time is one second, we can calculate power as:
\[ P = \frac{W}{t} \]

**Note**: This is a simplified model assuming no energy loss due to friction or air resistance.

Expert Solution

Step 1: Given data

Mass is $m equals 30 space kg$

In one second $t equals 1 space straight s$ , the vertical distance covered is $h equals 20 space straight m$

Note:

Gravitational acceleration is $g equals 9.8 space straight m divided by straight s squared$

$1 space straight N equals 1 space kg times straight m divided by straight s squared$

$1 space straight J equals 1 space Nm$

$1 space straight W equals 1 space straight J divided by straight s$

Find:

Power needed for the water pump.

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