300 kg sailboat accelerates at 0.5 m/s^2 at an angle of 25degrees North of East. Find the magnitude and direction of the force responsible for this accelereation.
F = M*a = 300 * 0.5[25o] = 150N,[25o] N. of E.
Well, let me just put on my sailor hat and calculate the force for you!
To find the magnitude of the force responsible for the acceleration, we can use Newton's second law of motion: F = ma, where F is the force, m is the mass, and a is the acceleration.
Given that the mass of the sailboat is 300 kg and the acceleration is 0.5 m/s², plugging these values into the formula, we get:
F = (300 kg) × (0.5 m/s²)
F = 150 N
So, the magnitude of the force responsible for the acceleration is 150 Newtons.
Now, let's find the direction. The sailboat is accelerating at an angle of 25 degrees north of east. I'm not sure why the sailboat wants to go north when it could go east and hit up the beach, but hey, everyone makes their own choices!
To find the direction of the force, we need to break it down into its x-component and y-component.
The x-component of the force can be found using the formula Fx = F × cos(angle), where Fx is the x-component of the force. Plugging in the values:
Fx = 150 N × cos(25°)
Fx ≈ 135.55 N
So, the x-component of the force is approximately 135.55 Newtons.
The y-component of the force can be found using the formula Fy = F × sin(angle), where Fy is the y-component of the force. Plugging in the values:
Fy = 150 N × sin(25°)
Fy ≈ 63.15 N
So, the y-component of the force is approximately 63.15 Newtons.
Therefore, the force responsible for the acceleration of the sailboat is approximately 135.55 Newtons directed east and approximately 63.15 Newtons directed north.
To find the magnitude and direction of the force responsible for the acceleration of the sailboat, we can break it down into its horizontal and vertical components.
Given:
Mass of the sailboat, m = 300 kg
Acceleration, a = 0.5 m/s^2
Angle, θ = 25 degrees north of east
Step 1: Find the horizontal component of the acceleration
The horizontal component of the acceleration can be found using the formula:
ah = a * cos(θ)
ah = 0.5 * cos(25)
ah ≈ 0.452 m/s^2
Step 2: Find the vertical component of the acceleration
The vertical component of the acceleration can be found using the formula:
av = a * sin(θ)
av = 0.5 * sin(25)
av ≈ 0.214 m/s^2
Step 3: Find the horizontal component of the force
Since the only force acting horizontally is the x-component of the force, we can use Newton's second law:
Fh = m * ah
Fh = 300 * 0.452
Fh ≈ 135.6 N
Step 4: Find the vertical component of the force
Since the only force acting vertically is the y-component of the force, we can use Newton's second law:
Fv = m * av
Fv = 300 * 0.214
Fv ≈ 64.2 N
Step 5: Find the magnitude of the force
The magnitude of the force can be calculated using the Pythagorean theorem:
F = √(Fh^2 + Fv^2)
F = √(135.6^2 + 64.2^2)
F ≈ 148.4 N
Step 6: Find the direction of the force
The direction of the force can be found using trigonometry:
Θ = tan^(-1)(Fv / Fh)
Θ = tan^(-1)(64.2 / 135.6)
Θ ≈ 25.67 degrees
The magnitude of the force responsible for the acceleration of the sailboat is approximately 148.4 N, and the direction is approximately 25.67 degrees north of east.
To find the magnitude and direction of the force responsible for the acceleration of the sailboat, we can use Newton's second law of motion. According to Newton's second law, the force acting on an object is equal to the mass of the object multiplied by its acceleration.
Given:
Mass of the sailboat (m) = 300 kg
Acceleration (a) = 0.5 m/s^2
Step 1: Calculate the magnitude of the force
Using Newton's second law, we can calculate the magnitude of the force (F) as follows:
F = m * a
Substituting the given values:
F = 300 kg * 0.5 m/s^2
F = 150 kg * m/s^2
The magnitude of the force responsible for the acceleration of the sailboat is 150 kg*m/s^2.
Step 2: Determine the direction of the force
The angle provided (25 degrees North of East) gives us the direction of the force. To express the direction, we usually break it down into its component vectors: one along the East-West axis (x-direction) and the other along the North-South axis (y-direction).
In this case, the force can be broken down into two components:
F_x = F * cos(25 degrees)
F_y = F * sin(25 degrees)
Substituting the value of F:
F_x = 150 kg*m/s^2 * cos(25 degrees)
F_y = 150 kg*m/s^2 * sin(25 degrees)
Calculating these values, we get:
F_x ≈ 136.646 kg*m/s^2
F_y ≈ 63.993 kg*m/s^2
Therefore, the magnitude of the force acting on the sailboat is approximately 150 kg*m/s^2, and its direction is approximately 136.646 kg*m/s^2 North of East in the x-direction and 63.993 kg*m/s^2 North of East in the y-direction.