Newton's Third Law: Acceleration of box and worker

[mitchy16]

Homework Statement

On a horizontal frictionless floor, a worker of weight 0.900 kN pushes horizontally with a force of 0.200 kN on a box weighing 1.80 kN. As a result of this push, which statement could be true?
A ) The box will not move because the push is less than its weight.
B ) The worker will accelerate at 2.17 m/s2 and the box will accelerate at 1.08 m/s2, but in opposite directions.
C ) The worker and box will both have an acceleration of 2.17 m/s2, but in opposite directions.
D ) The worker and box will both have an acceleration of 1.08 m/s2, but in opposite directions.
E ) The worker will accelerate at 1.08 m/s2 and the box will accelerate at 2.17 m/s2, but in opposite directions.

Homework Equations

F=ma
F_{A on B} = -F_{B on A}

The Attempt at a Solution

(converted all kN to N first)
Solving for mass:
WORKER:
w = mg
900N = m(9.8m/s²)
91.836 kg = m
BOX:
w = mg
1800N = m(9.8m/s²)
183.67 = m

Solving for acceleration:
WORKER:
F=ma
200 = (91.836)(a)
2.17 = a
BOX:
F=ma
-200=(183.67)(a)
-1.08 = a

I got the answer B, which is correct but why is it correct? I did all the work and got it, but why is it not A? Is it because Newton's third law? Sorry, just don't understand why this is correct.

 

[Nugatory]

There are three different forces acting on the box. What are they and what do they add up to? If the sum is non-zero then the box will accelerate.

There are three different forces acting on the worker. What are they and what do they add up to? If the sum is non-zero then the worker will accelerate.

Yes, you will need Newton's third law to identify some of these forces.

 

[haruspex]

why is it not A

Because forces and accelerations are vectors - direction matters.