Answer:
The magnitude of the vector sum of A and B is 65.8 cm and its direction 61.6°
Explanation:
Since vector A has magnitude 50 cm and a direction of 30, its x - component is A' = 50cos30 = 43.3 cm and its y - component is A" = 50sin30 = 25.
Also, Since vector B has magnitude 35 cm and a direction of 110, its x - component is A' = 35cos110 = -11.97 cm and its y - component is A" = 35sin110 = 32.89 cm.
So, the vector sum R = A + B
The x-component of the vector sum is R' = A'+ B' = 43.3 cm + (-11.97 cm) = 43.3 cm - 11.97 cm = 31.33 cm
The y-component of the vector sum is R" = A"+ B" = 25 cm + 32.89 cm = 57.89 cm
So, the magnitude of R = √(R'² + R"²)
= √((31.33 cm)² + (57.89 cm)²)
= √(981.5689 cm² + 3,351.2521 cm²)
= √(4,332.821 cm²)
= 65.82 cm
≅ 65.8 cm
The direction of R is Ф = tan⁻¹(R"/R')
= tan⁻¹(57.89 cm/31.33 cm)
= tan⁻¹(1.84775)
= 61.58°
≅ 61.6°
So, the magnitude of the vector sum of A and B is 65.8 cm and its direction 61.6°
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