So I used Fx = F1 cos x + F2 cos x and Fy = F1 sin x + F2 sinx to find F = (20 i

Question

So I used Fx = F1 cos x + F2 cos x and Fy = F1 sin x + F2 sinx to find F = (20 i + 15 j)N with M = 5.00 kg
so, I got a = 4i + 3j
but the back of the answer got a = 5m/s^2 at direction 36.869degree; I understand how they got there, using the magnitude ofacceleration and inverse tan ^-1. But why couldn't we just stop at a = 4i + 3j since we found the accelerationalready?

Explanation / Answer

Resultant force F = Fx i + Fyj The component of force along x-direction is     Fx = F1 + F2 cos90 = F1 = 20 N Along the vertical direction      Fy = F2 = 15 N ==> F = 20 i N + 15j N ==> a = F / m = a = 4i + 3j The magnitude of the acceleration          | a | = [4*4 + 3*3] = 25 = 5m/s2 When two forces acting on the object then object have theexperiences the magnitude of there resultant acceleration.

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