vector-components-worksheet 2.pdf - Ph 12 Vector Components Find ... - Free Printable

It looks like you've uploaded an image of a worksheet titled "Ph.1 Vector Components", which asks to find the vertical and horizontal components of various vectors given their magnitude and direction (angle). Since I can't view images directly, I'll help you solve this type of problem step by step based on what's typically found in such worksheets.

Let me explain how to solve these kinds of vector component problems and then walk through a few examples based on common setups.

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🔷 How to Find Horizontal and Vertical Components of a Vector

For a vector with:
- Magnitude: $ V $
- Angle: $ \theta $ (measured from the positive x-axis, usually counterclockwise)

The components are:

- Horizontal (x) component:
$$
V_x = V \cdot \cos(\theta)
$$

- Vertical (y) component:
$$
V_y = V \cdot \sin(\theta)
$$

> ✔ Always make sure your calculator is in degree mode unless otherwise specified.

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Now let’s go through some typical problems from your worksheet. Based on the layout, here are likely examples (I’ll reconstruct them from standard formats):

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📌 Example 1:

Vector: $ 50 \text{ N} $ at $ 30^\circ $

- $ V_x = 50 \cos(30^\circ) = 50 \times \frac{\sqrt{3}}{2} \approx 43.3 \text{ N} $
- $ V_y = 50 \sin(30^\circ) = 50 \times 0.5 = 25.0 \text{ N} $

✔ Answer:
- Horizontal: 43.3 N
- Vertical: 25.0 N

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📌 Example 2:

Vector: $ 80 \text{ m/s} $ at $ 60^\circ $

- $ V_x = 80 \cos(60^\circ) = 80 \times 0.5 = 40.0 \text{ m/s} $
- $ V_y = 80 \sin(60^\circ) = 80 \times \frac{\sqrt{3}}{2} \approx 69.3 \text{ m/s} $

✔ Answer:
- Horizontal: 40.0 m/s
- Vertical: 69.3 m/s

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📌 Example 3:

Vector: $ 100 \text{ N} $ at $ 45^\circ $

- $ V_x = 100 \cos(45^\circ) = 100 \times \frac{\sqrt{2}}{2} \approx 70.7 \text{ N} $
- $ V_y = 100 \sin(45^\circ) = 100 \times \frac{\sqrt{2}}{2} \approx 70.7 \text{ N} $

✔ Answer:
- Horizontal: 70.7 N
- Vertical: 70.7 N

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📌 Example 4:

Vector: $ 25 \text{ m} $ at $ 120^\circ $ (in second quadrant)

Note: $ 120^\circ $ is measured from positive x-axis → cosine will be negative, sine positive.

- $ V_x = 25 \cos(120^\circ) = 25 \times (-0.5) = -12.5 \text{ m} $
- $ V_y = 25 \sin(120^\circ) = 25 \times \frac{\sqrt{3}}{2} \approx 21.7 \text{ m} $

✔ Answer:
- Horizontal: -12.5 m
- Vertical: 21.7 m

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📌 Example 5:

Vector: $ 30 \text{ N} $ at $ 225^\circ $ (third quadrant)

- $ V_x = 30 \cos(225^\circ) = 30 \times (-\frac{\sqrt{2}}{2}) \approx -21.2 \text{ N} $
- $ V_y = 30 \sin(225^\circ) = 30 \times (-\frac{\sqrt{2}}{2}) \approx -21.2 \text{ N} $

✔ Answer:
- Horizontal: -21.2 N
- Vertical: -21.2 N

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📌 Example 6:

Vector: $ 40 \text{ km/h} $ at $ 330^\circ $ (fourth quadrant)

- $ V_x = 40 \cos(330^\circ) = 40 \times \cos(-30^\circ) = 40 \times \frac{\sqrt{3}}{2} \approx 34.6 \text{ km/h} $
- $ V_y = 40 \sin(330^\circ) = 40 \times (-0.5) = -20.0 \text{ km/h} $

✔ Answer:
- Horizontal: 34.6 km/h
- Vertical: -20.0 km/h

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✔ Summary of Steps:

1. Identify magnitude and angle.
2. Use:
- $ V_x = V \cos(\theta) $
- $ V_y = V \sin(\theta) $
3. Pay attention to quadrant signs:
- Q1: both +
- Q2: x–, y+
- Q3: both –
- Q4: x+, y–

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If you can provide the specific values from your worksheet (e.g., magnitudes and angles), I can give exact answers for each one.

Alternatively, if you describe or list the problems, I’ll solve them all!