Three vectors, expressed in Cartesian coordinates. What is the angle of the resultant vector S, T, U measured from the positive x axis?
x-comp y-comp
S -3.5 +4.5
T 0 -6.5
U +5.5 -2.5
To find the resultant, i'm assuming I have to add the columns up. If that's the case I got x-comp: 2 and y-comp: -2.25.
From there I figured I'd have to do
sqrt of (2^2 + -2.25^2)
which equals to 3.004.
I'm not sure how to get the angle though.
X = -3.5 + 0 + 5.5 = 2.0
Y = 4.5 -6.5 -2.5 = -4.5
Tan A = Y/X = -4.5/2 = -2.250
A = -66.0 CW = 294o CCW.
Well, my friend, you're on the right track with finding the magnitude of the resultant vector using the Pythagorean theorem. Now, to find the angle, we can use some trigonometry.
The angle θ can be calculated using the formula θ = arctan(y-comp / x-comp). Plugging in your values, we get θ = arctan(-2.25 / 2).
Now, beware of the tangent function's periodic nature. It has infinite solutions but we'll consider the principal value. Using a handy calculator, we find θ ≈ -48.99 degrees.
So, the angle of the resultant vector, measured from the positive x-axis, is approximately -48.99 degrees. Just remember that this is a positive value if measured counterclockwise from the positive x-axis, and negative if measured clockwise.
Hope that helps!
To find the angle of the resultant vector, you can use the inverse tangent (arctan) function.
First, calculate the angle θ using the formula:
θ = arctan(y-comp / x-comp)
In this case, the x-comp is 2 and the y-comp is -2.25:
θ = arctan(-2.25 / 2)
Using a calculator or trigonometric table, you will find that:
θ = -50.2 degrees (approximately)
Since the question asks for the angle measured from the positive x-axis, you need to consider the quadrant in which the resultant vector lies.
Since the x-comp is positive and the y-comp is negative, the resultant vector lies in the fourth quadrant.
To measure the angle from the positive x-axis, you need to add 180 degrees to the calculated angle:
θ = -50.2 degrees + 180 degrees
Therefore, the angle of the resultant vector S + T + U measured from the positive x-axis is approximately 129.8 degrees.
To find the angle of the resultant vector, you can use the inverse tangent function. Here's how you can do it:
1. Calculate the x-component and y-component of the resultant vector by adding up the corresponding components of the given vectors:
x-component: -3.5 + 0 + 5.5 = 2
y-component: 4.5 - 6.5 - 2.5 = -4.5
2. Use these values to find the magnitude (length) of the resultant vector:
magnitude = sqrt((x-component)^2 + (y-component)^2)
= sqrt((2)^2 + (-4.5)^2)
= sqrt(4 + 20.25)
= sqrt(24.25)
≈ 4.925
3. Finally, use the inverse tangent function (atan or arctan) to find the angle of the resultant vector from the positive x-axis:
angle = atan(y-component / x-component)
= atan(-4.5 / 2)
≈ -1.107 radians or approximately -63.43 degrees (rounded to two decimal places)
Note that the inverse tangent function (atan) returns an angle in radians. If you prefer the result in degrees, you can convert it by multiplying the radian measure by 180 degrees and dividing by π (pi).