A 16000 kg sailboat experiences an eastward force of 17700 N due to tide pushing its hull while the wind pushes the sails with a force of 87500 N directed toward the northwest (45 degrees westward of North or 45 degrees northward of West). What is the magnitude of the resultant acceleration of the sailboat? Answer in units of m/s^2.
I'm not sure what equation to be using with this.
m = 16000kg.
X = hor = 17700 + 87500cos(90+45),
X = 17700 - 61872 = -44172N.
Y = ver = 87500sin(90+45),
Y = 61872N.
(Fr)^2 = X^2 + Y^2,
(Fr)^2 = (-44172)^2 + (61872)^2,
(Fr)^2 = 5,779,309,968,
Fr = 76022N. = Resultant force.
a = Fr / m = 76022 / 16000 = 4.75m/s^2.
To determine the magnitude of the resultant acceleration of the sailboat, we need to combine the individual forces acting on it. We can use vector addition to determine the net force, and then apply Newton's second law, F = ma, to calculate the magnitude of the resultant acceleration.
Let's break down the given forces and their components:
1. The eastward force due to tide is 17,700 N.
2. The wind force is 87,500 N directed toward the northwest, which makes it 45 degrees westward of North or 45 degrees northward of West.
To find the horizontal component of the wind force, we can use the cosine function:
Horizontal component of wind force = 87,500 N * cos(45 degrees)
To find the vertical component of the wind force, we can use the sine function:
Vertical component of wind force = 87,500 N * sin(45 degrees)
Now we have all the components of the forces:
- Eastward force due to tide: 17,700 N (horizontal component) and 0 N (vertical component).
- Wind force:
- Horizontal component: 87,500 N * cos(45 degrees).
- Vertical component: 87,500 N * sin(45 degrees).
To find the net force, we need to sum up the horizontal and vertical components of all the forces acting on the sailboat. Then we can use Newton's second law to calculate the magnitude of the resultant acceleration:
Net horizontal force = Sum of all the horizontal components of the forces.
Net vertical force = Sum of all the vertical components of the forces.
Next, we use Newton's second law, F = ma, to find the magnitude of the resultant acceleration:
Resultant acceleration = Net force / mass
Given that the mass of the sailboat is 16,000 kg, we can substitute the known values into the equation to find the resultant acceleration.