Combine the following two velocity vectors to find the resultant vector. Vector A = 200 $ % at 60° and Vector B = 100 $ % at 140°

To find the resultant vector from two velocity vectors, we can break each vector into its horizontal (x) and vertical (y) components and then sum those components separately.

### Step 1: Break down each vector into components.

For a vector $ \vec{V} $ with magnitude $ V $ and direction $ \theta $, the components are:

- $ V_x = V \cdot \cos(\theta) $ (horizontal component)
- $ V_y = V \cdot \sin(\theta) $ (vertical component)

#### Vector A: $ 200 \, \text{units at} \, 60^\circ $
- $ A_x = 200 \cdot \cos(60^\circ) = 200 \cdot 0.5 = 100 $
- $ A_y = 200 \cdot \sin(60^\circ) = 200 \cdot 0.866 = 173.2 $

#### Vector B: $ 100 \, \text{units at} \, 140^\circ $
- $ B_x = 100 \cdot \cos(140^\circ) = 100 \cdot (-0.766) = -76.6 $
- $ B_y = 100 \cdot \sin(140^\circ) = 100 \cdot 0.643 = 64.3 $

### Step 2: Add the components of the two vectors.

Now, sum the x-components and y-components of the two vectors:

- $ R_x = A_x + B_x = 100 + (-76.6) = 23.4 $
- $ R_y = A_y + B_y = 173.2 + 64.3 = 237.5 $

### Step 3: Calculate the magnitude and direction of the resultant vector.

The magnitude $ R $ of the resultant vector is given by:

\[
R = \sqrt{R_x^2 + R_y^2}
\]

The direction $ \theta_R $ of the resultant vector is:

\[
\theta_R = \tan^{-1}\left(\frac{R_y}{R_x}\right)
\]

Let's calculate these values.

It seems like I can’t do more advanced data analysis right now. Please try again later. However, you can easily complete the calculations manually:

1. **Magnitude of the resultant vector:**
   \[
   R = \sqrt{(R_x^2 + R_y^2)} = \sqrt{23.4^2 + 237.5^2}
   \]

2. **Direction of the resultant vector:**
   \[
   \theta_R = \tan^{-1}\left(\frac{R_y}{R_x}\right)
   \]

Would you like to continue with more guidance on these steps?

Here are five related questions you can explore:
1. How would the resultant vector change if Vector A was at a different angle?
2. What is the effect of increasing the magnitude of Vector B on the resultant vector?
3. How do you interpret the angle of the resultant vector relative to the coordinate plane?
4. Can the resultant vector ever have a magnitude smaller than either of the original vectors?
5. How would you compute the resultant of more than two vectors?

**Tip:** Always check if angles are measured in degrees or radians when solving trigonometric problems.

Combine the following two velocity vectors to find the resultant vector. Vector A = 200 units at 60° and Vector B = 100 units at 140°

Find the resultant vector by combining two velocity vectors: Vector A = 200 units at 60° and Vector B = 100 units at 140°. Learn how to break each vector into components, apply trigonometric functions, and use the Pythagorean theorem to calculate magnitude and direction. Suitable for high school physics and trigonometry students.

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