friction pushes east
east
The force of friction will push the cart to the east, which is opposite to the direction the cart is being pushed. Friction always acts in the direction opposite to the direction of motion.
East
northwest
most likely pushed west to east
The wheels of the cart will rotate in the same direction that the cart is being pushed, so they will also go towards the west.
You must discard something. Give something some momentum in one direction, and that gives the rest of you momentum in the opposite direction. - Turn your head left and exhale, then turn your head right and inhale, repeat until arrival at bank. - Throw something. Coat, keys, spit, etc. IF you have nothing, chew off a leg. Throwing something results in an equal momentum imparted to you in the opposite direction. If you threw something west, then you'd go east.
When the Earth rotates from west to east, it produces wind in east to west direction and because of this friction occurs in between them which has turned the Earth round in shape.
If something is being carried by westerlies, it is moving from west to east. Westerlies are prevailing winds that flow from the west to the east in the mid-latitudes.
When waves from the South West strike a beach running East to West, the longshore current is likely to flow Eastward along the shore. This is because the waves will push the water along the coast in that direction due to the angle of wave approach and the prevailing wind direction causing the net movement of water along the shore to the East.
Cartage was almost directly south from Rome, but it was slightly to the West so something like South-South-West would be quite correctly.
Something being carried by westerlies is moving from west to east. Westerlies are prevailing winds that blow from the west towards the east in the mid-latitudes of both the Northern and Southern Hemispheres.