The resultant<span> is the vector sum of 2 or more vectors. It is the conclusion of adding 2 or more vectors together. If </span>displacement <span>vectors A, B, and C are added together, the result will be vector R.</span>
So the ball velocity changes from 10m/s into the wall to -8m/s in a totally opposite direction within a time span of 0.012s. Then we can calculate the average acceleration of the ball as the change in velocity over a unit of time.
Since the goal of the airbag is helping the person to stop after the collision in a greater time, this means that the change in momentum must finish when this is just zero.
In other words, the change in momentum, must be equal to the initial one, but with opposite sign.
Now, just applying the original form of Newton's 2nd Law, we know that this change in momentum must be equal to the impulse needed to stop the person:
So, as we know the magnitude of Δp from (1) and we have different Δt as givens, we can get the different values of F (in magnitude) required to stop the person for each one of them, as follows: