F = 32N[30o] + 56N[0o]? + 38N[60o] = 27.7+16i + 56 + 19+32.9i = 102.7 + 48.9i = 118N{25.5o].
F = M*a, a = F/M = 118[25.5o]/118 = 1 m/s^2[25.5o].
Three astronauts, propelled by jet backpacks, push and guide a 118 kg asteroid toward a processing dock, exerting the forces shown in the figure, with F1 = 32 N, F2 = 56 N, F3 = 38 N, θ1 = 30°, and θ3 = 60°. What is the (a) magnitude and (b) angle (measured relative to the positive direction of the x axis in the range of (-180°, 180°]) of the asteroid's acceleration?
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