Explanation:
1. To graphically add vectors, use the tail-to-tip method. Draw the first vector (it doesn't matter which), then draw the second vector where the first vector ends. The resultant vector is from the tail of the first vector to the tip of the second vector.
This graph shows two ways to get the resultant: A + B or B + A.
desmos.com/calculator/bqhcclhhqc
2. To algebraically add vectors, split each vector into x and y components.
Aₓ = 5.0 cos 45 = 3.5
Aᵧ = 5.0 sin 45 = 3.5
Bₓ = 2.0 cos 180 = -2.0
Bᵧ = 5.0 sin 180 = 0
The components of the resultant vector are the sums of the components of A and B.
Cₓ = 3.5 + -2.0 = 1.5
Cᵧ = 3.5 + 0 = 3.5
The magnitude of the resultant vector is found with Pythagorean theorem, and the direction is found with tangent.
C = √(Cₓ² + Cᵧ²) ≈ 3.9 m/s
θ = atan(Cᵧ / Cₓ) ≈ 67°
