Conclusion:
The total net force acting on the objects is 16 N, directed towards the right.
Clarification:
It is stated that,
The force exerted by the dog,
(to the right)
The force exerted by Simone,
(backward)
Here, assume the backward direction is negative and the right direction is positive.
The net force will move in the direction where the larger force is present. The net force can be calculated as:


F = 16 N
Thus, the net force amounts to 16 N, acting towards the right.
The rocket's acceleration is described here as

now recognizing that

we integrate both sides



given that the rocket is accelerating for a duration of t = 10 s
thus, we have


consequently, after t = 10 s, the rocket will achieve a speed of 130 m/s in an upward direction