To solve this problem, we can use the principle of conservation of momentum, which states that the total momentum of a system remains constant unless acted on by an external force. In this case, the initial momentum of the car before the collision is 3,565 kg * 27.2 m/s = 97,068 kgm/s, and the initial momentum of the truck before the collision is 0 kgm/s, since it is stationary. After the collision, the two vehicles become stuck together and move away from the point of impact with a combined mass of 3,565 kg + 3,692 kg = 7,257 kg. Since the total momentum of the system must remain constant, the combined velocity of the two vehicles after the collision must be equal to the total initial momentum of the car and truck before the collision, or 97,068 kg*m/s.
Therefore, the combined velocity of the two vehicles after the collision is 97,068 kg*m/s / 7,257 kg = 13.4 m/s. This is the speed at which the two vehicles move away from the point of impact. Note that this is a bit less than half the initial speed of the car before the collision, which is expected since the combined mass of the car and truck is greater than the mass of the car alone, and the momentum of the system must be conserved.