wHAT ARE THE x and y COMPONENTS OF A 25m DISPLACEMENT AT AN ANGLE OF 210degree with the x-axis(clockwise and anticlockwise)

To find the x and y components of a displacement vector, we can use trigonometric functions. In this case, we have a displacement of 25 meters at an angle of 210 degrees measured clockwise from the positive x-axis. Let's break this down step by step.

Understanding the Angle and Components

The angle of 210 degrees is located in the third quadrant of the Cartesian coordinate system. In this quadrant, both the x and y components of the vector will be negative. To find the components, we can use the cosine and sine functions:

• x-component: This can be calculated using the cosine function.
• y-component: This can be calculated using the sine function.

Calculating the Components

The formulas for the components are as follows:

• x = r * cos(θ)
• y = r * sin(θ)

Where:

• r = magnitude of the displacement (25 m)
• θ = angle in radians (for calculations, we need to convert degrees to radians if necessary)

Conversion of Degrees to Radians

To convert degrees to radians, we use the formula:

radians = degrees × (π / 180)

For 210 degrees:

θ = 210 × (π / 180) = 7π/6 radians

Finding the x and y Components

Now we can plug the values into the formulas:

• x = 25 * cos(210°)
• y = 25 * sin(210°)

Using the known values of cosine and sine for 210 degrees:

• cos(210°) = -√3/2
• sin(210°) = -1/2

Substituting these values in:

• x = 25 * (-√3/2) = -12.5√3 ≈ -21.65 m
• y = 25 * (-1/2) = -12.5 m

Final Results

Thus, the x and y components of the 25 m displacement at an angle of 210 degrees are approximately:

• x-component: -21.65 m
• y-component: -12.5 m

This means the displacement vector points towards the third quadrant, confirming our earlier understanding of the angle's position. If you have any further questions or need clarification on any part of this process, feel free to ask!