Name: __________________________________________ Date: _________________________ Pd: __________
Accelerated Physics
Mr. Roberts
Algebraic Vector Addition Worksheet
On a separate piece of paper algebraically determine the magnitude of the resultant vector from the vectors
given. Using SOHCAHTOA and Pythagorean Theorem, find the x & y components of each vector. For each
problem, list the resultant vector in component AND polar form. Turn in all work.
Problem #1: A + B
Vector A = 15 m East (0o)
Vector B = 5.6 m Northeast (no angle assumes 45o)
Resultant Vector:
𝑅⃑ = ___________________ 𝑥̂ + __________________ 𝑦̂
𝑅⃑ = ____________________ , 𝜃𝑅 = ____________________
Problem #2: D + E
Vector D = 13 m/s 330o
Vector E = 6 m/s 135 o
Resultant Vector:
𝑅⃑ = ___________________ 𝑥̂ + __________________ 𝑦̂
𝑅⃑ = ____________________ , 𝜃𝑅 = ____________________
Problem #3: 1 + 2 + 3
Vector 1 = 12 Newtons 180 o
Vector 2 = 9.0 Newtons 140o
Vector 3 = 3.0 Newtons 230o
Resultant Vector:
𝑅⃑ = ___________________ 𝑥̂ + __________________ 𝑦̂
𝑅⃑ = ____________________ , 𝜃𝑅 = ____________________
Problem #4: F + G + H + I
Vector F = 2.5 m/s2 N
Vector G = 4.5 m/s2 SW
Vector H = 3.0 m/s2 NW
Vector I = 3.0 m/s2 E
Resultant Vector:
𝑅⃑ = ___________________ 𝑥̂ + __________________ 𝑦̂
𝑅⃑ = ____________________ , 𝜃𝑅 = ____________________
Problem #5: 4 – 5 + 6 – 7
Vector 4 = 3.0 m W
Vector 5 = 10 .0 m S
Vector 6 = 12.0 m NW
Vector 7 = 3.0 m SW
Resultant Vector:
𝑅⃑ = ___________________ 𝑥̂ + __________________ 𝑦̂
𝑅⃑ = ____________________ , 𝜃𝑅 = ____________________
Problem #6: A – B + C
Vector A = 20 m @ 45o NE
Vector B = 6.0 m South
Vector C = 10.0 m @ 45o SE
Resultant Vector:
𝑅⃑ = ___________________ 𝑥̂ + __________________ 𝑦̂
𝑅⃑ = ____________________ , 𝜃𝑅 = ____________________
Problem #7: B – A
Vector A = 250 m/s West
Vector B = 100 m/s NE
Resultant Vector:
𝑅⃑ = ___________________ 𝑥̂ + __________________ 𝑦̂
𝑅⃑ = ____________________ , 𝜃𝑅 = ____________________
Problem #8: A + B – C
Vector A = 1.60 m/s SE
Vector B = 3.5 m/s SW
Vector C = 3.0 m.s South
Resultant Vector:
𝑅⃑ = ___________________ 𝑥̂ + __________________ 𝑦̂
𝑅⃑ = ____________________ , 𝜃𝑅 = ____________________