please help

find the resultant of these two vectors: 2.00 * 10^2 units due east and 4.00 * 10^2 units 30.0degrees north of west

please show me step by step how to do this
thanks for any help!

200

Well, well, well, let's calculate the resultant vector together. Step right up to the circus of vectors!

First, let's break down those two vectors:

Vector A has a magnitude of 200 units and points due east (let's call it positive x direction).

Vector B has a magnitude of 400 units and points 30.0 degrees north of west.

Now, let's find the horizontal and vertical components of Vector B:

Horizontal component (Bx):
Bx = B * cos(theta)
Bx = 400 * cos(30.0°)

Vertical component (By):
By = B * sin(theta)
By = 400 * sin(30.0°)

Now, it's time to add the horizontal components:

Ax + Bx = 200 + Bx

And the vertical components:

By - Ay = By - 0 (since Vector A has no vertical component)

Now, let's put it all together:

Resultant = sqrt((Ax + Bx)^2 + (By - Ay)^2)

Now, don't worry, I won't make you perform tedious calculations. Just plug in the values and let the numbers dance their way to the answer!

And voila! You've just finished your high-flying act of vector addition. Make sure to practice your balance before the next show!

Sure! To find the resultant of two vectors, we can use the graphical method or the component method. Let's use the component method since it's generally more straightforward.

Step 1: Understanding the Problem
First, we need to understand the given information. We have two vectors:
- Vector A: 2.00 * 10^2 units due east
- Vector B: 4.00 * 10^2 units 30.0 degrees north of west

Step 2: Resolve the Vectors into x and y Components
Next, we need to break down both vectors into their x (horizontally) and y (vertically) components.

For Vector A, which is due east, the x-component is its magnitude multiplied by the cosine of 0° (since east is along the x-axis, which has an angle of 0°), and the y-component is 0.

For Vector B, which is 30 degrees north of west, we need to find the x and y components using trigonometry. The x-component is the magnitude multiplied by the cosine of the angle 30° (since it is west, which is along the negative x-axis), and the y-component is the magnitude multiplied by the sine of the angle 30° (since it is north, which is along the positive y-axis).

Step 3: Calculate the Components
Using the given magnitudes and angles, we can calculate the components:

For Vector A:
x-component of A = magnitude of A * cos(0°) = 2.00 * 10^2 * cos(0°) = 2.00 * 10^2
y-component of A = magnitude of A * sin(0°) = 2.00 * 10^2 * sin(0°) = 0

For Vector B:
x-component of B = magnitude of B * cos(30°) = 4.00 * 10^2 * cos(30°) = 3.46 * 10^2
y-component of B = magnitude of B * sin(30°) = 4.00 * 10^2 * sin(30°) = 2.00 * 10^2

Step 4: Add the Components
To find the resultant, we need to add the x-components and y-components separately.

Resultant (x-component) = x-component of A + x-component of B = (2.00 * 10^2) + (3.46 * 10^2) = 5.46 * 10^2
Resultant (y-component) = y-component of A + y-component of B = (0) + (2.00 * 10^2) = 2.00 * 10^2

Step 5: Calculate the Magnitude and Direction of the Resultant
To find the resultant magnitude, we use the Pythagorean theorem:

Resultant Magnitude = sqrt((Resultant (x-component))^2 + (Resultant (y-component))^2)
= sqrt((5.46 * 10^2)^2 + (2.00 * 10^2)^2)
= sqrt(29.8816 * 10^4 + 4.00 * 10^4)
= sqrt(33.8816 * 10^4)
= sqrt(338816)
≈ 582.21

To find the resultant direction, we use the inverse tangent (arctan) of the y-component divided by the x-component:

Resultant Direction = arctan((Resultant (y-component)) / (Resultant (x-component)))
= arctan((2.00 * 10^2) / (5.46 * 10^2))
= arctan(0.366) ≈ 20.39°

Step 6: Interpret the Result
The resultant of the given two vectors has a magnitude of approximately 582.21 units and is directed approximately 20.39 degrees north of east.

Remember, these calculations assume that the given vectors are added using the standard rules of vector addition.

Add the vectors

Resultant=200E+400 @30 N of W
= 200E+ 400Cos30 W + 400Sin30N
= -200W+ 346W + 200N combine the West units, and that is it. Now if you want to express it as a direction, then
= 146W+ 200N
find the angle N of W (angle=arctan146/200= 36.1 deg N of W)
and the magnitude, use Pyth theorm, or
magnitude = 200/cos36.1=247
check that