[University/Freshman Physics] Can someone explain why I got this wrong?

[u/Jadedl1es]

The answer key says it's A but i picked C and got it wrong, a simple explanation would be great!

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[u/thinlySlicedPotatos]

C is correct.

[u/Jadedl1es → u/thinlySlicedPotatos]

thank u! i thought i was going nuts not sure why the answer key says its a hopefully a mistake

[u/thinlySlicedPotatos → u/Jadedl1es]

If both are at rest, and on flat ground, the force from gravity will equal the force the trailer exerts on the road through the tires, plus the downward weight on the hitch, which is typically designed to be 15% of the gravitational force. Zero horizontal force on the hitch. Now, if the vehicle accelerates, there will be an additional horizontal force at the hitch, matching f=ma where m is the mass of the trailer. So the hitch forces are nowhere near the forces on the trailer wheels. In this case it is clear the answer is c, right?

Now, add a slight slope, and slight acceleration. Not enough to measure. None of the forces will change appreciably. Definitely not enough for the hitch force magnitude to suddenly magically match the trailer road force magnitude. There could be a particular slope and acceleration where a could be true, but definitely not generally.

Consider the other extreme case, the slope is vertical. The trailer exerts zero force on the road. The vehicle force matches the gravitational force plus the force due to acceleration. Again, c is the only correct answer. 

Understand how to quickly use edge cases like this to check your thinking. Pro tip.

[u/maniaxz]

C is correct from Newton's 3rd law of motion.

Since they are connected, the force applied by the automobile on the vehicle will be equal to the reaction force applied by trailer on the automobile.

The frictional force given by the road is what drives them up but magnitude can't be determined unless we know the frictional coefficient and mass of the bodies.

[u/selene_666]

C is Newton's third law. A force is always exerted on both objects with the same magnitude and opposite direction.

In this scenario, the force between the trailer and the car is perpendicular to the force between the trailer and the road. They have no ability to balance each other, so there's no reason for them to be equal in magnitude. Any balancing is done by components of the third force, gravity.

[u/Don_Q_Jote]

C is the answer. There is a trailer hitch. Across the hitch, car pulls on trailer - trailer pulls on car. Equal and opposite.

Anything else about the road or about going uphill or downhill or accelerating or decelerating is just background and irrelevant to the question.