To solve this problem, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision, assuming no external forces are acting on the system.
First, let's convert the velocities of the car and truck from km/h to m/s for consistency:
Car velocity (v1) = 90.0 km/h = 25.0 m/s (Westward) Truck velocity (v2) = 72.0 km/h = 20.0 m/s (Eastward)
The momentum (p) of an object is given by the product of its mass (m) and velocity (v): p = mv.
Let's calculate the initial momentum (p_initial) and final momentum (p_final) of the system:
Initial momentum (p_initial) = momentum of car + momentum of truck = (mass of car * velocity of car) + (mass of truck * velocity of truck) = (1500 kg * (-25.0 m/s)) + (1400 kg * 20.0 m/s) = -37,500 kg·m/s + 28,000 kg·m/s = -9,500 kg·m/s (Westward - Eastward = Westward)
Since the car and truck entangle and move off together, their combined mass is 1500 kg + 1400 kg = 2900 kg.
Final momentum (p_final) = momentum of wreckage = (mass of wreckage * velocity of wreckage)
Using the principle of conservation of momentum, we equate the initial and final momentum:
p_initial = p_final -9,500 kg·m/s = (2900 kg * velocity of wreckage)
Solving for the velocity of wreckage (v_wreckage):
velocity of wreckage (v_wreckage) = -9,500 kg·m/s / 2900 kg ≈ -3.28 m/s
The negative sign indicates that the wreckage is moving in the opposite direction of the car's initial velocity, which is eastward. Therefore, the velocity of the wreckage immediately after the collision is approximately 3.28 m/s eastward.