Solved PHYS-103 Name: Physics: Vector Addition Worksheet | Chegg.com - Free Printable

I'll solve this physics worksheet on vector addition by finding the x and y components of each vector and then adding the vectors as requested.

Let me start by examining the first part: finding the x and y components of each vector.

For a vector with magnitude V at an angle θ from the positive x-axis:
- x-component = V × cos(θ)
- y-component = V × sin(θ)

First vector (12 m/s at 30°):
- x = 12 × cos(30°) = 12 × (√3/2) ≈ 12 × 0.866 = 10.39 m/s
- y = 12 × sin(30°) = 12 × 0.5 = 6.00 m/s

Second vector (25 m/s at 60°):
- x = 25 × cos(60°) = 25 × 0.5 = 12.50 m/s
- y = 25 × sin(60°) = 25 × (√3/2) ≈ 25 × 0.866 = 21.65 m/s

Third vector (15 m/s at 150°):
- x = 15 × cos(150°) = 15 × (-√3/2) ≈ 15 × (-0.866) = -12.99 m/s
- y = 15 × sin(150°) = 15 × 0.5 = 7.50 m/s

Now, let's move to Part II: Adding the vectors.

First pair of vectors:
Vector 1: 12 m/s at 20°
- x₁ = 12 × cos(20°) ≈ 12 × 0.940 = 11.28 m/s
- y₁ = 12 × sin(20°) ≈ 12 × 0.342 = 4.10 m/s

Vector 2: 12 m/s at 70°
- x₂ = 12 × cos(70°) ≈ 12 × 0.342 = 4.10 m/s
- y₂ = 12 × sin(70°) ≈ 12 × 0.940 = 11.28 m/s

Resultant:
- x_total = x₁ + x₂ = 11.28 + 4.10 = 15.38 m/s
- y_total = y₁ + y₂ = 4.10 + 11.28 = 15.38 m/s

Second pair of vectors:
Vector 1: 50 m at 135°
- x₁ = 50 × cos(135°) = 50 × (-√2/2) ≈ 50 × (-0.707) = -35.36 m
- y₁ = 50 × sin(135°) = 50 × (√2/2) ≈ 50 × 0.707 = 35.36 m

Vector 2: 30 m at 90° (straight up)
- x₂ = 30 × cos(90°) = 30 × 0 = 0 m
- y₂ = 30 × sin(90°) = 30 × 1 = 30 m

Resultant:
- x_total = x₁ + x₂ = -35.36 + 0 = -35.36 m
- y_total = y₁ + y₂ = 35.36 + 30 = 65.36 m

This completes the solution for the vector addition worksheet.