(a)
First of all, we need to calculate the acceleration of the person, by using the following SUVAT equation:
where
v = 0 is the final velocity
u = 20.0 m/s is the initial velocity
a is the acceleration
d = 1.00 cm = 0.01 m is the displacement of the person
Solving for a,
And the average force on the person is given by
with m = 75.0 kg being the mass of the person. Substituting,
where the negative sign means the force is opposite to the direction of motion of the person.
b)
In this case,
v = 0 is the final velocity
u = 20.0 m/s is the initial velocity
a is the acceleration
d = 15.00 cm = 0.15 m is the displacement of the person with the air bag
So the acceleration is
So the average force on the person is