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A vector has a magnitude 40 m and is at an angle of 125 degrees to the positive x−axis. Calculate its x and y components.

User Lxgr
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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

User Caleb Faruki
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