a boat has a mass of 6800 kg. its engine generate a drive force of 4100 N, due west, while the wind exerts a force of 8000 N, due east, and the water exerts a resistive force of 1200 N due east. what is the magnitude and direction of the boats accelerations? (answer 0.309 m/s^2) I need a step by step help please
Find net force: -4100N + 800N + 1200N= -2100N
F=ma
-2100N = 6800kg x a
/6800 kg /6800kg
-2100N/6800kg = a
a = -0.31
Ahoy, matey! Let's set sail through this problem, one step at a time!
First, let's break down the forces acting on the boat:
- The engine generates a drive force of 4100 N to the west.
- The wind exerts a force of 8000 N to the east.
- The water exerts a resistive force of 1200 N to the east.
To find the boat's acceleration, we need to calculate the net force acting on it. The net force is the sum of all forces acting on the boat.
Here's how we can calculate it:
1) Calculate the total force due to wind and water:
- Since both the wind and the water exert forces in the same direction (east), we add them together:
Total force = force due to wind + force due to water
Total force = 8000 N + 1200 N
Total force = 9200 N to the east
2) Calculate the net force by considering the drive force and the total force:
- Since the drive force is acting in the opposite direction (west) to the total force, we subtract them:
Net force = drive force - total force
Net force = 4100 N - 9200 N
Net force = -5100 N
Note: The negative sign indicates that the net force is in the opposite direction to the drive force.
3) Next, we need to calculate the boat's acceleration using Newton's Second Law of Motion, which states:
Net force = mass * acceleration
Rearranging the formula, we can solve for acceleration:
acceleration = net force / mass
acceleration = -5100 N / 6800 kg
acceleration ≈ -0.75 m/s²
Now, let's convert this negative acceleration into its magnitude (positive value):
magnitude of acceleration = |-0.75|
magnitude of acceleration ≈ 0.75 m/s²
As you mentioned that the answer is 0.309 m/s², there may be a mistake in the calculations or a misunderstanding in the problem. Remember that the direction of the acceleration will be in the opposite direction to the net force, while the magnitude will be a positive value.
I hope these steps help you navigate your way to the correct answer!
To find the magnitude and direction of the boat's acceleration, we need to consider the net force acting on the boat. Newton's second law states that the net force acting on an object is equal to its mass multiplied by its acceleration.
Step 1: Determine the net force acting on the boat.
The boat experiences three forces: the drive force from the engine, the force from the wind, and the resistive force from the water. Since these forces act in opposite directions, we need to subtract the forces that are acting in the opposite direction.
Net force = Drive force - Wind force - Water resistive force
Given:
Drive force (F_drive) = 4100 N (due west)
Wind force (F_wind) = 8000 N (due east)
Water resistive force (F_resist) = 1200 N (due east)
Net force = 4100 N - 8000 N - 1200 N
Step 2: Calculate the net force.
Net force = -5100 N (Since the forces in opposite directions, we consider the negative sign for the net force)
Step 3: Calculate the acceleration.
Use Newton's second law:
Net force = mass × acceleration
Given:
Mass of the boat (m) = 6800 kg
Substitute the known values:
-5100 N = 6800 kg × acceleration
Solve for acceleration:
acceleration = -5100 N / 6800 kg
acceleration ≈ -0.75 m/s² (Note that acceleration is negative because the net force is in the opposite direction of the drive force)
Step 4: Find the magnitude of the acceleration.
The magnitude of acceleration is the absolute value of the acceleration calculated in the previous step:
Magnitude of acceleration = |-0.75 m/s²|
Magnitude of acceleration ≈ 0.75 m/s²
Step 5: Determine the direction of the acceleration.
Since the acceleration is negative, it indicates that the boat is decelerating (or experiencing retardation). The direction of the acceleration is in the same direction as the net force, which is due east.
Conclusion:
The magnitude of the boat's acceleration is approximately 0.75 m/s², and its direction is due east.
Fn = -4100 + 8000 + 1200 = 5100 N., Due
East. = Net force.
a = Fn/m = 5100/6800 = 0.75 m/s^2, Due
East.