WAEC Physics 2011 Theory — Question 2
Question 2 of 39 from the West African Examinations Council (WAEC) Physics 2011 Theory paper, with the correct answer and a full explanation.
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1(b) Three vectors 3ms⁻¹ N45°W, 12ms⁻¹ W and 5ms⁻¹ S act at a point. (i) Sketch a vector diagram to illustrate the given information. (ii) Calculate the resultant of the vectors.
Model answer
Resolving into horizontal and vertical components: V1(3ms⁻¹, N45°W): horizontal = -3sin45° = -2.12, vertical = 3cos45° = 2.12. V2(12ms⁻¹, W): horizontal = -12, vertical = 0. V3(5ms⁻¹, S): horizontal = 0, vertical = -5. Sum: Vx = -14.12, Vy = -2.88. Resultant V = sqrt(Vx² + Vy²) = sqrt(14.12² + 2.88²) = sqrt(199.37+8.29) = sqrt(207.66) = 14.4 m/s. Direction: tanθ = 2.88/14.12 = 0.204, θ = 11.53°. Resultant v = 14.4m/s, W11.53°S (or S78.65°W).
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