The correct answer to the question is A): The truck and trailer will experience a net force of 40 newtons backward.
EXPLANATION:
As per the question, the force exerted by the truck F = 2750 N forward.
The force exerted by the trailer F' = 2790 N backward.
We are asked to calculate the net force experienced by the truck and trailer.
From above, we see that two forces are anti parallel i.e they are opposite to each other.
Hence, the angle between them [tex]\theta = 180^{0}[/tex].
Let the magnitude of the resultant force is R.
From parallelogram law of vector addition, the magnitude of the resultant is calculated as -
[tex]R=\ \sqrt{F^2+F'^2+2FF'cos\theta}[/tex]
= [tex]\sqrt{F^2+F'^2+2FF'cos180}[/tex]
= [tex]\sqrt{F^2+F'^2-2FF'}[/tex]
= [tex]\sqrt{(F'-F)^2}[/tex]
= F' - F
= 2790 N - 2750 N
= 40 N. [ans]
The direction of resultant of two anti parallel vectors will be along the direction of bigger vector.
Hence, the net force will be 40 N backward.
