Newton's Second Law and jetpacks

[suspenc3]

Three astronauts, propelled by jetpacks, push a 120kg asteroid toward a processing dock, exerting the forces
F1 = 32N at 30 degrees above the horizontal
F2 = 55N on the horizontal
F3 = 41N below 60 degrees below the horizontal

what is the asteroids acceleration in unit vector notation?

m = 120kg
F2 = (5N)i

F1+F2+F3 = ma

F1 = (32N cos30deg) , (32N sin30deg)
F1 = (27.7)i + 16j

F3 = (41N cos-60deg) , (41N sin-60deg)
F3 = (20.5N)i - (35.5N)j

Fnet = ma
Fnet/m = a
(27.7/120 +55 + 20.5/120)i , (-35.5/120 + 16/120)j = a

Is this right so far?

 

[Fermat]

Apart from a couple of typos, yes it's correct.

 

[quicknote]

Yes, your approach is correct so far. However, there is a small mistake in your calculation of F3. The correct components of F3 would be (20.5N)i + (35.5N)j. This is because the angle of -60 degrees is in the fourth quadrant, where the y-component should be positive. So the correct equation would be:

F3 = (41N cos(-60deg))i + (41N sin(-60deg))j
F3 = (20.5N)i + (35.5N)j

From here, you can continue with your calculation of the net force and acceleration in unit vector notation.