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.
FA on B = -FB on A
The Attempt at a Solution
(converted all kN to N first)
Solving for mass:
w = mg
900N = m(9.8m/s2)
91.836 kg = m
w = mg
1800N = m(9.8m/s2)
183.67 = m
Solving for acceleration:
200 = (91.836)(a)
2.17 = 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.