A 2200-kg sport utility vehicle traveling at 96 km/h can be stopped in 0.15 s if it hits a concrete wall. Assume a 60 kg person was in the car that hit this wall. The velocity of the person equals that of the car both before and after the crash, and the velocity changes in 0.15 s.

To solve this problem, we need to use the principle of conservation of momentum and the equation of motion.

First, let's find the initial momentum of the car-person system. The momentum is given by the product of mass and velocity. The mass of the car is 2200 kg and the velocity is 96 km/h, which we need to convert to m/s:

Initial momentum = (mass of car + mass of person) * velocity
= (2200 kg + 60 kg) * (96 km/h * (1000 m/1 km) * (1 h/3600 s))
= 2260 kg * (96 * 1000/3600) m/s
= 2260 kg * 26.67 m/s
≈ 60,202 kg·m/s

Next, let's find the final velocity of the car-person system after the crash. We know that the velocity of the car and the person are the same, so we can assume the final velocity of the system is v.

Using the equation of motion (Δv = displacement/time), we can find the acceleration of the car-person system during the collision:

Δv = (final velocity - initial velocity)
Δv = (v - 96 km/h * (1000 m/1 km) * (1 h/3600 s))
Δv = v - 26.67 m/s

The time taken for the velocity to change is 0.15 s. Therefore, we can write:

Δv = acceleration * time
v - 26.67 m/s = acceleration * 0.15 s

Solving this equation for acceleration, we get:

acceleration = (v - 26.67 m/s) / 0.15 s

Now, let's use the principle of conservation of momentum to find the final momentum of the car-person system:

Final momentum = Initial momentum

(mass of car + mass of person) * final velocity = 60,202 kg·m/s

Substituting in the final velocity equation, we have:

(2200 kg + 60 kg) * ((v - 26.67 m/s) / 0.15 s) = 60,202 kg·m/s

Now, we can solve this equation for the final velocity of the car-person system (v):

(2260 kg) * ((v - 26.67 m/s) / 0.15 s) = 60,202 kg·m/s

Divide both sides by 2260 kg:

((v - 26.67 m/s) / 0.15 s) = 60,202 kg·m/s / 2260 kg

Simplify:

v - 26.67 m/s = (60,202 kg·m/s) / (2260 kg) * 0.15 s
v - 26.67 m/s = (60202 kg·m/s / 2260 kg) * 0.15 s

Multiply the fractions:

v - 26.67 m/s = 0.99912 m/s

Adding 26.67 m/s to both sides:

v = 26.67 m/s + 0.99912 m/s

v ≈ 27.67 m/s

Therefore, the final velocity of the car-person system after the crash is approximately 27.67 m/s.