An automobile accident causes both the driver and passenger front airbags to deploy.

a. If the vehicle travelled at a speed of 88.6 km/h is now at rest, find the change in momentum for both the 68.4 kg adult driver and the 34.2 kg child passenger.
b. The adult took 0.564 s and the child took 0.260 s to come to rest. Find the force that the airbag exerted on each individual. Explain why airbags tend to be dangerous to children.

a. To find the change in momentum for each individual, we can use the equation:

Change in momentum = mass × final velocity - mass × initial velocity

Given:
- Mass of the adult driver (m1) = 68.4 kg
- Mass of the child passenger (m2) = 34.2 kg
- Initial velocity (u) = 88.6 km/h (convert to m/s: 88.6 km/h × 1000 m/1 km × 1/3600 h/1 s = 24.6 m/s)
- Final velocity (v) = 0 m/s (since the vehicle is at rest)

For the adult driver:
Change in momentum (Δp1) = m1 × v - m1 × u
= 68.4 kg × 0 m/s - 68.4 kg × 24.6 m/s
= -68.4 kg × 24.6 m/s
= -1685.44 kg·m/s

For the child passenger:
Change in momentum (Δp2) = m2 × v - m2 × u
= 34.2 kg × 0 m/s - 34.2 kg × 24.6 m/s
= -34.2 kg × 24.6 m/s
= -840.12 kg·m/s

Therefore, the change in momentum for the adult driver is -1685.44 kg·m/s and for the child passenger is -840.12 kg·m/s.

b. To find the force exerted by the airbag on each individual, we can use the equation:

Force (F) = Change in momentum (Δp) / Time (t)

Given:
- Time taken for the adult to come to rest (t1) = 0.564 s
- Time taken for the child to come to rest (t2) = 0.260 s

For the adult driver:
Force exerted by airbag on the adult (F1) = Δp1 / t1
= (-1685.44 kg·m/s) / (0.564 s)
= -2988.68 N (negative sign indicates the direction of force)

For the child passenger:
Force exerted by airbag on the child (F2) = Δp2 / t2
= (-840.12 kg·m/s) / (0.260 s)
= -3230.46 N (negative sign indicates the direction of force)

Therefore, the force exerted by the airbag on the adult driver is -2988.68 N and on the child passenger is -3230.46 N.

Airbags tend to be dangerous to children because they are designed to protect adults who are taller and heavier. The force exerted by the airbag depends on the change in momentum and the time taken for the person to come to rest. Children have smaller mass and differently proportioned bodies compared to adults, so the force exerted by the airbag may be too strong for a child's body to handle. This can lead to injuries such as fractures or internal damage due to the excessive force being applied to a smaller body. It is important for children to use appropriate child seats or boosters to ensure their safety in vehicles.