(a) Since we are given all of the forces acting on the rocket, then we can use the definition of net force to find the net force on the rocket. Begin by sketching the forces.
Figure: Freebody diagram for the rocket.
To find the net force, add the vectors tail to head. The resultant, drawn from the tail of the first vector to the head of the last vector, is the net force and points upward.
Figure: Net force on the rocket.
Now, solve for the net force algebraically by summing all forces acting on the rocket.
Check the answer. The net force has an upward (+y) component which agrees with the picture.
(b) To calculate the final momentum of the rocket, use the {\b momentum principle}. First, define the system.
Next, write the momentum principle and solve for the final momentum. This is called the update form of the momentum principle.
Substitute the initial momentum and net force.
Always check the answer and compare it to a picture. In this case, the initial momentum of the rocket is upward, and the net force on the rocket is upward. Because of the momentum principle, its change in momentum must also be upward, in the same direction as the net force. Thus, to draw the final momentum vector, place the change in momentum at the head of the initial momentum vector, and draw the final momentum vector from the tail of the initial momentum to the head of the change in momentum. You will notice that it is upward and larger than the initial momentum, exactly as we calculated.
Figure: Net force on the rocket.
