1) A force vector has a magnitude of 579 newtons and points at an angle 43o of below the positive x axis.
Find the x scalar component and the y scalar component of the vector?
For the x component I did 579cos(43) = 423.45 N. Is this correct?
For the y component I did 579sin(43) but this was incorrect. I am not sure what to do.
The angle is -43°, not 43°
The vector points below the x-axis, so sin is negative.
To find the x scalar component of the force vector, you correctly used the equation:
x component = magnitude * cos(angle) = 579 N * cos(43°) = 423.45 N.
To find the y scalar component of the force vector, you need to use the sine function. However, when calculating the sine component, you have to take into account the direction of the y-axis.
Since the force vector points below the positive x-axis, the y scalar component will be negative. Therefore, you need to use the equation:
y component = - magnitude * sin(angle) = -579 N * sin(43°) = -392.00 N (rounded to two decimal places).
So, the correct y scalar component of the vector is -392.00 N.
To find the x and y scalar components of a vector, you can use trigonometry. The x scalar component represents the projection of the vector onto the x-axis, while the y scalar component represents the projection of the vector onto the y-axis.
For the x component, you correctly used the formula: x component = magnitude * cos(angle). By substituting the values you provided, it would be:
x component = 579 N * cos(43°) ≈ 423.45 N
So, your calculation for the x component is correct.
Now, let's calculate the y component. Since the angle is measured below the positive x-axis, it becomes a downward angle. In trigonometry, angles below the x-axis are usually considered negative. Therefore, to calculate the y component, you'll need to use the sine function with the negative angle:
y component ≈ 579 N * sin(-43°)
Using a scientific calculator or the sine function on your calculator, calculate sin(-43°). Note that some calculators may require you to enter the angle in radians, in which case you need to convert it first. Make sure you are using the appropriate unit (degrees or radians) for your calculator.
So, the correct calculation for the y component would be:
y component ≈ 579 N * sin(-43°) ≈ -427.08 N
Therefore, the correct x scalar component is approximately 423.45 N, and the correct y scalar component is approximately -427.08 N.