A vector has a magnitude of 18.2 cm and makes an angle of 129.0° with the positive x-axis. What are the x- and y-components of this vector
x: 18.2 cos 129 = -18.2 cos51
= -11.45 cm
y: 18.2 sin 129 = 18.2 sin51
= 14.14 cm
To find the x- and y-components of the vector, we can use trigonometry.
The x-component of the vector can be found by taking the magnitude of the vector and multiplying it by the cosine of the angle with the positive x-axis.
x-component = magnitude * cos(angle)
In this case, the magnitude of the vector is given as 18.2 cm and the angle is given as 129.0°.
x-component = 18.2 cm * cos(129.0°)
Using a scientific calculator, evaluate the cosine of 129.0°, which is approximately -0.575 (rounded to three decimal places).
x-component ≈ 18.2 cm * (-0.575)
The x-component of the vector is approximately -10.485 cm (rounded to three decimal places).
Now, let's find the y-component of the vector. The y-component can be found by taking the magnitude of the vector and multiplying it by the sine of the angle with the positive x-axis.
y-component = magnitude * sin(angle)
Using the same values as above:
y-component = 18.2 cm * sin(129.0°)
Evaluate the sine of 129.0°, which is approximately 0.818 (rounded to three decimal places).
y-component ≈ 18.2 cm * 0.818
The y-component of the vector is approximately 14.883 cm (rounded to three decimal places).
So, the x-component of the vector is approximately -10.485 cm and the y-component is approximately 14.883 cm.