find the x- and y- component of vector R which has a length of 13cm at 30.0 degrees
It depends on where the 30 degrees is measured from. If from the x axis, in a counter clockwise direction, then
x= 13cm*cos30
y= 13cm*sin30
To find the x- and y-components of vector R, we need to use the given length and angle. Here's how you can do it step-by-step:
Step 1: Convert the angle from degrees to radians.
The given angle is 30.0 degrees.
To convert from degrees to radians, we can use the formula: radians = degrees * (π/180).
Plugging in the values, we have: radians = 30.0 * (π/180).
Simplifying, we get: radians ≈ 0.5236.
Step 2: Calculate the x-component of vector R.
The x-component can be found by multiplying the length of vector R by the cosine of the angle.
The formula is: x-component = length * cos(angle).
Plugging in the values, we have: x-component = 13cm * cos(0.5236).
Evaluating the cosine function, we get: x-component ≈ 11.213cm.
Step 3: Calculate the y-component of vector R.
The y-component can be found by multiplying the length of vector R by the sine of the angle.
The formula is: y-component = length * sin(angle).
Plugging in the values, we have: y-component = 13cm * sin(0.5236).
Evaluating the sine function, we get: y-component ≈ 6.5cm.
Therefore, the x-component of vector R is approximately 11.213 cm and the y-component is approximately 6.5 cm.
To find the x- and y-component of vector R, we can use trigonometric functions and the given information.
Let's consider vector R as a straight line segment starting from the origin (0,0) and ending at the point (x,y). The length of vector R is given as 13 cm, and the angle it makes with the positive x-axis is 30.0 degrees.
The x-component (Rx) of vector R can be found by multiplying the length of R by the cosine of the angle:
Rx = Length of R * cos(Angle)
Rx = 13 cm * cos(30.0°)
Remember to use the appropriate trigonometric function depending on whether you are working with degrees or radians. In most calculators, you can switch between degrees and radians mode.
Now, let's calculate Rx:
Rx = 13 cm * cos(30.0°)
Rx = 13 cm * 0.866 (cosine of 30.0 degrees is approximately 0.866)
Rx ≈ 11.258 cm
So, the x-component of vector R is approximately 11.258 cm.
Similarly, the y-component (Ry) of vector R can be found by multiplying the length of R by the sine of the angle:
Ry = Length of R * sin(Angle)
Ry = 13 cm * sin(30.0°)
Now, let's calculate Ry:
Ry = 13 cm * sin(30.0°)
Ry = 13 cm * 0.5 (sine of 30.0 degrees is 0.5)
Ry = 6.5 cm
So, the y-component of vector R is 6.5 cm.
Therefore, the x- and y-components of vector R with a length of 13 cm at 30.0 degrees are approximately 11.258 cm and 6.5 cm respectively.