Halliday, Resnick & Walker — Force and Motion-I: Problem 5

5 Three astronauts, propelled by jet backpacks, push and guide a 120 kg asteroid toward a processing dock, exerting the forces shown in Fig. 5-19, with $F_1 = 32\text{ N}$, $F_2 = 55\text{ N}$, $F_3 = 41\text{ N}$, $\theta_1 = 30^\circ$, and $\theta_3 = 60^\circ$. What is the asteroid’s acceleration (a) in unit-vector notation and as (b) a magnitude and (c) a direction relative to the positive direction of the $x$ axis?