To find the east component of the vector, we can break down the velocity vector (50 m/s at 35° from the east direction) into its horizontal (east) and vertical (south) components using trigonometry.

The east component $v_{\text{east}}$ is the horizontal component of the velocity vector, which can be calculated using the cosine function:

$v_{\text{east}} = v \cdot \cos(\theta)$

Where:

• $v = 50 \, \text{m/s}$ (the magnitude of the vector),
• $\theta = 35^\circ$ (the angle from east),
• $\cos(\theta)$ is the cosine of the angle.

Now, calculate:

$v_{\text{east}} = 50 \cdot \cos(35^\circ)$

Using a calculator:

$v_{\text{east}} \approx 50 \cdot 0.8192 = 40.96 \, \text{m/s}$

So, the east component of the vector is approximately 40.96 m/s.

Would you like more details on the calculations or have any other questions?

Here are 5 follow-up questions to expand on this:

1. How do you calculate the south component of the vector?
2. What is the total velocity if we know both the east and south components?
3. How would the result change if the angle was different?
4. Can you explain the significance of the cosine and sine functions in vector decomposition?
5. How can this concept apply in real-world scenarios, like navigation?

Tip: To decompose any vector, remember that the horizontal (east-west) component uses cosine, and the vertical (north-south) component uses sine.