https://file.aiquickdraw.com/mathbot/file/1727185269025ftbhd891.jpg

x = 1759 m/s East  ; vy =1500 m/s North

vx = 2598 m/s  East  ; vy =1500 m/s North

vx = 1500 m/s East ; vy =2598 m/s North

vx =  866 m/s East  ; vy =2598 m/s North

To find the horizontal (\( v_x \)) and vertical (\( v_y \)) components of the velocity vector \( \vec{V} \) shown in the diagram, we will use the following trigonometric relationships:

Given:
- Resultant velocity (\( V \)) = 3000 m/s
- Angle (\( \theta \)) = 30 degrees (North of East)

### Formulas:
1. **Horizontal component** (\( v_x \)):
   \[
   v_x = V \cdot \cos \theta
   \]
2. **Vertical component** (\( v_y \)):
   \[
   v_y = V \cdot \sin \theta
   \]

### Calculation:
1. **Horizontal component**:
   \[
   v_x = 3000 \cdot \cos(30^\circ) = 3000 \cdot \frac{\sqrt{3}}{2} \approx 2598 \text{ m/s}
   \]

2. **Vertical component**:
   \[
   v_y = 3000 \cdot \sin(30^\circ) = 3000 \cdot \frac{1}{2} = 1500 \text{ m/s}
   \]

### Answer:
- \( v_x = 2598 \text{ m/s East} \)
- \( v_y = 1500 \text{ m/s North} \)

So, the correct option is:

**Option 2: \( v_x = 2598 \text{ m/s East} \); \( v_y = 1500 \text{ m/s North} \)**

Would you like more details or have any questions about this solution? Here are 5 related questions to consider:

1. How do we determine the direction of each component in terms of East and North?
2. What is the significance of the angle being North of East?
3. How would the components change if the angle were 45 degrees instead of 30 degrees?
4. Can we use the Pythagorean theorem to verify the magnitude of the resultant velocity?
5. How does the choice of coordinate axes affect the calculation of components?

**Tip:** Remember that the cosine and sine functions help decompose vectors into their respective horizontal and vertical components.

The above diagram shows a resultant velocity of 3000 m/s at an angle of 30 degrees North of East. What is the horizontal component (v_x) and vertical component (v_y)?

Learn how to decompose a velocity vector of 3000 m/s at 30 degrees North of East into horizontal and vertical components. Using trigonometric formulas, this problem helps students understand vector decomposition and its applications in physics.

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