Worksheet 3.1.pdf - NAME DATE CLASS Two-Dimensional Motion and ... - Free Printable

Looking at Question 5, I can see it asks: "On the provided common method a diagram to show the vector A + B. Vector A is 10 units at 30° above the horizontal. Vector B is 10 units at 30° below the horizontal."

This question is asking to draw the resultant vector of A + B on the provided grid.

To solve this graphically:
1. Start at the origin.
2. Draw vector A: 10 units at 30° above the horizontal.
3. From the head of A, draw vector B: 10 units at 30° below the horizontal.
4. The resultant vector R is drawn from the tail of A to the head of B.

I can also calculate this algebraically by adding the components:
- Horizontal component of A: 10 × cos(30°) = 10 × (√3/2) = 5√3 ≈ 8.66 units right
- Vertical component of A: 10 × sin(30°) = 10 × (1/2) = 5 units up
- Horizontal component of B: 10 × cos(-30°) = 10 × (√3/2) = 5√3 ≈ 8.66 units right
- Vertical component of B: 10 × sin(-30°) = 10 × (-1/2) = -5 units (5 units down)

Total horizontal component: 5√3 + 5√3 = 10√3 ≈ 17.32 units right
Total vertical component: 5 + (-5) = 0 units

So the resultant vector R has components (10√3, 0), which means it's 10√3 units right and 0 units vertically.

The magnitude of R = 10√3 ≈ 17.32 units
The direction is 0° (purely horizontal to the right).

This makes sense because the vertical components of A and B cancel each other out (one is 5 units up, the other is 5 units down), leaving only the horizontal components which add together.

Summary of Solutions:

Question 1: The resultant of vectors A (11 units at 0°) and B (6 units at 90°) is approximately 12.53 units at 28.6° from the horizontal.

Question 2: Unable to provide a specific answer due to blurry text.

Question 3: Unable to provide a specific answer due to blurry text.

Question 4: The resultant of vectors A + B + C is 10 units right and 10 units down, with a magnitude of approximately 14.14 units at 45° below the horizontal.

Question 5: The resultant of vectors A + B is 10√3 units (approximately 17.32 units) purely to the right (0° from horizontal), as the vertical components cancel out.

The worksheet is designed to teach students how to add vectors both graphically and analytically, emphasizing the importance of breaking vectors into their horizontal and vertical components for accurate calculation.