To solve this problem, we can apply the principle of conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after the collision, provided there are no external forces acting on the system.
The momentum (p) of an object is given by the product of its mass (m) and velocity (v): p = m * v.
Let's calculate the momentum of the car and truck before the collision:
Momentum of the car = mass of the car * velocity of the car = 1500 kg * 90.0 km/h
Momentum of the truck = mass of the truck * velocity of the truck = 1400 kg * (-72.0 km/h) [Note: the truck is traveling in the opposite direction, so its velocity is negative.]
Now, since the car and truck entangle and head off as one, they have a combined mass of 1500 kg + 1400 kg = 2900 kg.
Let's find the velocity of the wreckage immediately after the collision using the principle of conservation of momentum:
Total momentum before the collision = Total momentum after the collision
(momentum of the car) + (momentum of the truck) = (momentum of the wreckage)
(1500 kg * 90.0 km/h) + (1400 kg * (-72.0 km/h)) = (2900 kg * v)
Now, let's convert the velocities from km/h to m/s:
90.0 km/h = 90.0 * (1000 m/3600 s) = 25 m/s 72.0 km/h = 72.0 * (1000 m/3600 s) = 20 m/s
Substituting the values:
(1500 kg * 25 m/s) + (1400 kg * (-20 m/s)) = (2900 kg * v)
37500 kgm/s - 28000 kgm/s = 2900 kg * v
9500 kg*m/s = 2900 kg * v
Dividing both sides by 2900 kg:
v = 9500 kg*m/s / 2900 kg
v ≈ 3.28 m/s
Therefore, the velocity of the wreckage immediately after the collision is approximately 3.28 m/s in the direction of the car's initial motion, which is west.