If the resultant r of 2 vectors is 48 centimeters north of east what are the x and y components of that vector?
Please proofread. That makes no sense. centimeters is distance, not angle.
It says if the resultant, r, of 2 vectors is 48 centimeters north of east, what is the x component of the vector and what is the y component.
I am sorry. That does not make sense to me.
as always, when measuring counterclockwise from the +x axis,
x = r cosθ
y = r sinθ
I’m confused because you usually are given the angle. If you go by the steps you put that gives 0 and 48 and that is not a correct answer choice.
I think it is a typo. You need both a length and an angle. In other words how far North of East :)
Try 45 degrees and see if that matches an answer.
The answer choices are 24, 50, 42, 36,21, and 16 and I need to know which one is x and which one is y.
It is a typo. 48 is given as your y component. The y component IS the distance North of East. I suspect they mean length of 48 cm at θ degrees North of East but forgot to give you θ
To determine the x and y components of a vector given its resultant and direction, we can use trigonometry.
Let's assume that the angle between the resultant vector and the positive x-axis is θ.
The x-component (Rx) can be determined by using the cosine function:
Rx = r * cos(θ)
Similarly, the y-component (Ry) can be determined using the sine function:
Ry = r * sin(θ)
In this case, the resultant r is given as 48 centimeters, and it is stated that the resultant is north of east. Since north is 90 degrees clockwise from the positive x-axis, θ would be 90 degrees.
Plugging the values into the formulas:
Rx = 48 * cos(90) = 0 centimeters
Ry = 48 * sin(90) = 48 centimeters
Therefore, the x-component of the vector is 0 centimeters, and the y-component is 48 centimeters.