Answer: To find the x and y components of a vector with a magnitude of 40 m and an angle of 125 degrees to the positive x-axis, you can use trigonometric functions. Here's how you can calculate the x and y components:
The x-component (Vx) can be found using the formula:
Vx = V * cos(θ)
Where:
V is the magnitude of the vector (40 m).
θ is the angle the vector makes with the positive x-axis (125 degrees).
Vx = 40 m * cos(125°)
Now, calculate Vx:
Vx = 40 m * cos(125°)
Vx ≈ 40 m * (-0.5736)
Vx ≈ -22.944 m (rounded to three decimal places)
So, the x-component of the vector is approximately -22.944 m.
The y-component (Vy) can be found using the formula:
Vy = V * sin(θ)
Where:
V is the magnitude of the vector (40 m).
θ is the angle the vector makes with the positive x-axis (125 degrees).
Vy = 40 m * sin(125°)
Now, calculate Vy:
Vy = 40 m * sin(125°)
Vy ≈ 40 m * 0.8192
Vy ≈ 32.768 m (rounded to three decimal places)
So, the y-component of the vector is approximately 32.768 m.
Therefore, the x and y components of the vector are approximately:
x-component (Vx) ≈ -22.944 m
y-component (Vy) ≈ 32.768 m