The magnitude of the x-component of the vector V is approximately 31.03 and the magnitude of the y-component is approximately 30.80.
The x-component:
- The x-component of a vector is represented by its projection onto the x-axis. In the image, the x-axis is horizontal. We can see that the vector V makes an angle of 30 degrees with the positive x-axis.
- To find the magnitude of the x-component, we can use the cosine function. The cosine of an angle represents the ratio of the adjacent side (the x-component in this case) to the hypotenuse (the magnitude of the vector V).
Therefore, the magnitude of the x-component (|Vx|) can be calculated as:
|Vx| = |V| * cos(30°)
where |V| is the magnitude of the vector V, which is given in the image as 35.80.
The y-component:
- The y-component of a vector is represented by its projection onto the y-axis. In the image, the y-axis is vertical. We can see that the vector V makes an angle of 60 degrees with the positive y-axis.
- To find the magnitude of the y-component, we can use the sine function. The sine of an angle represents the ratio of the opposite side (the y-component in this case) to the hypotenuse (the magnitude of the vector V).
Therefore, the magnitude of the y-component (|Vy|) can be calculated as:
|Vy| = |V| * sin(60°)
where |V| is again 35.80.
Calculations:
|Vx| = 35.80 * cos(30°) ≈ 31.03
|Vy| = 35.80 * sin(60°) ≈ 30.80