the wind blows with a force of 425N north on a sail boat, while the water exerts a force of 325N west on the sailboat. Find the magnitude and direction of the net external force on the sailboat.
magnitude= sqrt(425^2+325^2)
direction: arctheta(425/325) N of W
To find the magnitude and direction of the net external force on the sailboat, we can use vector addition.
Step 1: Draw a diagram representing the forces acting on the sailboat.
Draw a coordinate system with the x-axis representing east-west direction and the y-axis representing north-south direction. Now, draw arrows representing the wind force and water force according to their given magnitudes and directions.
The wind force (425N) is directed north, so draw an arrow pointing up on the y-axis. The water force (325N) is directed west, so draw an arrow pointing left on the x-axis.
Step 2: Resolve the forces into their components.
To resolve the forces, we need to split them into their x-axis (horizontal) and y-axis (vertical) components.
The wind force can be split into its components as follows:
- The y-component (north component) is the same as the magnitude of the force (425N) because it is directed along the y-axis.
- The x-component (east component) is 0N because it is not directed along the x-axis.
The water force can be split into its components as follows:
- The x-component (west component) is the same as the magnitude of the force (325N) because it is directed along the x-axis.
- The y-component (south component) is 0N because it is not directed along the y-axis.
Step 3: Add the x-components and y-components separately.
The x-components add up to -325N because the wind force has an x-component of 0N and the water force has an x-component of -325N.
The y-components add up to +425N because the wind force has a y-component of +425N and the water force has a y-component of 0N.
Step 4: Find the magnitude and direction of the net force.
To find the magnitude of the net force, we can use the Pythagorean theorem:
Magnitude = √(x-component^2 + y-component^2)
Magnitude = √((-325N)^2 + (425N)^2)
Magnitude = √(105625N^2 + 180625N^2)
Magnitude = √(286250N^2)
Magnitude = 535.73N (approx.)
To find the direction of the net force, we can use trigonometry:
Direction = arctan(y-component / x-component)
Direction = arctan(425N / -325N)
Direction = arctan(-1.31) (approx.)
Therefore, the magnitude of the net external force on the sailboat is approximately 535.73N, and the direction is arctan(-1.31).