A rocket car had a mass of 1650kg. The engine expels 140kg of combustion products in 7s. The expelled material has a velocity of 850m/s to the south. Calculate the velocity of the car at the end of 7s. ANSWER: 72m/s to the north

This is a type of collision, we will say that momentum is conserved.

Initial conditions
m1 = 1650kg v1=0m/s
Treat the thrust as a separate entity.
m2 = 140kg v2 = 850

Final conditions,
m1 = 1650 v1=?
Since the thrust is expelled its mass is nonexistant in the system therefore 0 momentum

(m1v1)initial + (m2v2)initial = (m1v1)final