An airboat with mass 960 kg, including the passengers, has a propeller that produces a driving horizontal force F₂ = 1680 N and water produces an average water resistance force FD=864 N as shown in the figure. What is the acceleration of the boat measured in m/s²?
An airboat with mass 960 kg, including the passengers, has a propeller that produces a driving horizontal force F₂ = 1680 N and water produces an average water resistance force FD=864 N as shown in the figure. What is the acceleration of the boat measured in m/s²?
Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
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Publisher:Raymond A. Serway, John W. Jewett
Chapter4: Motion In Two Dimensions
Section: Chapter Questions
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**Explanation of the Image:**
The image shows an airboat with a group of people on it. The boat has a large propeller at the back that produces a driving force \( F_p \), indicated by a yellow arrow pointing in the direction of the boat's movement. There is also a red arrow pointing in the opposite direction, representing the water resistance force \( F_D \).
**Question:**
What is the acceleration of the boat measured in m/s²?
---
**Solution:**
To find the acceleration of the boat, we can apply Newton's second law of motion:
\[ F_{net} = m \cdot a \]
Where \( F_{net} \) is the net force on the boat, \( m \) is the mass of the boat, and \( a \) is the acceleration of the boat.
First, calculate the net force \( F_{net} \):
\[ F_{net} = F_p - F_D \]
\[ F_{net} = 1680 \, \text{N} - 864 \, \text{N} \]
\[ F_{net} = 816 \, \text{N} \]
Next, solve for the acceleration \( a \):
\[ a = \frac{F_{net}}{m} \]
\[ a = \frac{816 \, \text{N}}{960 \, \text{kg}} \]
\[ a = 0.85 \, \text{m/s}^2 \]
The acceleration of the boat is \( 0.85 \, \text{m/s}^2 \).
---](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcde4937d-e883-446c-8941-8d2ade4d99b0%2F7ce974ab-4017-41c8-abf1-7021103eb33d%2F2lozd33_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 2-a, Numerical:
An airboat with mass 960 kg, including the passengers, has a propeller that produces a driving horizontal force \( F_p = 1680 \) N and water produces an average water resistance force \( F_D = 864 \) N as shown in the figure.
**Explanation of the Image:**
The image shows an airboat with a group of people on it. The boat has a large propeller at the back that produces a driving force \( F_p \), indicated by a yellow arrow pointing in the direction of the boat's movement. There is also a red arrow pointing in the opposite direction, representing the water resistance force \( F_D \).
**Question:**
What is the acceleration of the boat measured in m/s²?
---
**Solution:**
To find the acceleration of the boat, we can apply Newton's second law of motion:
\[ F_{net} = m \cdot a \]
Where \( F_{net} \) is the net force on the boat, \( m \) is the mass of the boat, and \( a \) is the acceleration of the boat.
First, calculate the net force \( F_{net} \):
\[ F_{net} = F_p - F_D \]
\[ F_{net} = 1680 \, \text{N} - 864 \, \text{N} \]
\[ F_{net} = 816 \, \text{N} \]
Next, solve for the acceleration \( a \):
\[ a = \frac{F_{net}}{m} \]
\[ a = \frac{816 \, \text{N}}{960 \, \text{kg}} \]
\[ a = 0.85 \, \text{m/s}^2 \]
The acceleration of the boat is \( 0.85 \, \text{m/s}^2 \).
---
The image shows an airboat with a propeller on the water. The driving force, \( F_p \), is indicated with a yellow arrow pointing forward, and the water resistance force, \( F_D \), is denoted with a red arrow pointing backward.
**Question:**
How long does it take (measured in seconds) to accelerate the airboat from rest to a speed of 12 m/s?
---
For educational purposes, this problem requires the application of Newton's Second Law of Motion to find the net force acting on the airboat and subsequently using kinematic equations to find the time taken to reach the given speed.
Steps to solve:
1. Calculate the net force acting on the airboat.
2. Use the net force to determine the acceleration.
3. Apply the kinematic equation to find the time taken to reach the speed of 12 m/s from rest.
### Solution:
1. **Calculate the Net Force:**
\[ F_{\text{net}} = F_p - F_D \]
\[ F_{\text{net}} = 1680 \, \text{N} - 864 \, \text{N} \]
\[ F_{\text{net}} = 816 \, \text{N} \]
2. **Determine the Acceleration:**
Using Newton's Second Law:
\[ F = ma \]
\[ a = \frac{F_{\text{net}}}{m} \]
\[ a = \frac{816 \, \text{N}}{960 \, \text{kg}} \]
\[ a = 0.85 \, \text{m/s}^2 \]
3. **Find the Time Using Kinematic Equation:**
Using the equation:
\[ v = u + at \]
Where:
\( v \) = final velocity = 12 m/s
\( u \) = initial velocity = 0 m/s (from rest)
\( a \) = acceleration = 0.85 m/s²
\[ 12 \,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcde4937d-e883-446c-8941-8d2ade4d99b0%2F7ce974ab-4017-41c8-abf1-7021103eb33d%2Fdqdoukk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 2-b, Numerical:
An airboat with a mass of 960 kg, including the passengers, has a propeller that produces a driving horizontal force \( F_p = 1680 \, \text{N} \), and the water produces an average water resistance force \( F_D = 864 \, \text{N} \) as shown in the figure.
The image shows an airboat with a propeller on the water. The driving force, \( F_p \), is indicated with a yellow arrow pointing forward, and the water resistance force, \( F_D \), is denoted with a red arrow pointing backward.
**Question:**
How long does it take (measured in seconds) to accelerate the airboat from rest to a speed of 12 m/s?
---
For educational purposes, this problem requires the application of Newton's Second Law of Motion to find the net force acting on the airboat and subsequently using kinematic equations to find the time taken to reach the given speed.
Steps to solve:
1. Calculate the net force acting on the airboat.
2. Use the net force to determine the acceleration.
3. Apply the kinematic equation to find the time taken to reach the speed of 12 m/s from rest.
### Solution:
1. **Calculate the Net Force:**
\[ F_{\text{net}} = F_p - F_D \]
\[ F_{\text{net}} = 1680 \, \text{N} - 864 \, \text{N} \]
\[ F_{\text{net}} = 816 \, \text{N} \]
2. **Determine the Acceleration:**
Using Newton's Second Law:
\[ F = ma \]
\[ a = \frac{F_{\text{net}}}{m} \]
\[ a = \frac{816 \, \text{N}}{960 \, \text{kg}} \]
\[ a = 0.85 \, \text{m/s}^2 \]
3. **Find the Time Using Kinematic Equation:**
Using the equation:
\[ v = u + at \]
Where:
\( v \) = final velocity = 12 m/s
\( u \) = initial velocity = 0 m/s (from rest)
\( a \) = acceleration = 0.85 m/s²
\[ 12 \,
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