Answer:
1. To calculate the change in momentum of the car, we need to use the formula:
Δp = m * Δv
where Δp is the change in momentum, m is the mass of the car, and Δv is the change in velocity.
At the moment of collision, the car is traveling at 100 km/h, which is 27.78 m/s. When the car comes to a standstill, its velocity is 0 m/s. So the change in velocity is:
Δv = 0 - 27.78 = -27.78 m/s
The mass of the car is 1200 kg. So the change in momentum is:
Δp = m * Δv = 1200 kg * (-27.78 m/s) = -33,336 kg m/s
Therefore, the change in momentum of the car is -33,336 kg m/s.
2. To determine the minimum velocity the car can slow down to during a collision with the barrels without the crash being fatal, we need to use the formula:
p = mv
where p is momentum, m is mass, and v is velocity.
The safety zone in terms of momentum is from 0 to 1000 kg/m/s. We know that the mass of an average person is 80 kg. So we can calculate the maximum momentum that an 80 kg person can safely withstand:
p_max = 80 kg * 1000 kg/m/s = 80,000 kg m/s
Now we can rearrange the formula to solve for the minimum velocity:
v_min = p_max / m
v_min = 80,000 kg m/s / 1200 kg
v_min = 66.67 m/s
Therefore, the minimum velocity that the car can slow down to during a collision with the barrels without the crash being fatal is 66.67 m/s.