Consider again the discussion in Section 7.2 concerning air bags and impulse for a car colliding with a tree. The car’s velocity of 40 mi/h is reduced to zero very quickly, but the head of a passenger is still moving at 40 mi/h (about 18 m/s). Calculate the average force exerted on the passenger’s head coming to rest for the case 

(a) when it is stopped by the dashboard in 5.0 ms and 

(b) when it is stopped by an air bag that compresses in 45 ms. 

(c) Air bags must deploy quickly. If the distance between the passenger’s head and the dashboard is 60 cm and it takes the air bag 45 ms to safely bring the passenger to rest, how much time is there for the air bag to inflate?