Final answer:
To find the truck's velocity after an elastic collision with a car, apply the conservation of momentum. The initial momentum of the system equals the final momentum. The truck's final velocity is determined by solving the momentum equation, resulting in approximately +15.7 meters/second, or answer C.
Step-by-step explanation:
The question is asking for the velocity of the truck after an elastic collision with a car. In an elastic collision, both momentum and kinetic energy are conserved.
Given the scenario where a car of mass 1.1 × 103 kg and initial velocity +22.0 m/s collides with a stationary truck of mass 2.3 × 103 kg, and the car's velocity after collision is -11.0 m/s, we can use conservation of momentum to solve for the truck's post-collision velocity.
The total momentum before the collision must equal the total momentum after the collision. Thus:
Initial momentum of car = (mass of car) × (initial velocity of car) = 1.1 × 103 kg × 22 m/s = 24200 kg·m/s.
Because the truck is initially stationary, its initial momentum is 0 kg·m/s.
After the collision, the car's momentum is (mass of car) × (final velocity of car) = 1.1 × 103 kg × (-11 m/s) = -12100 kg·m/s.
Let's denote the final velocity of the truck as Vt. The total momentum after the collision is the sum of the car's and truck's momentum: -12100 kg·m/s + (mass of truck) × Vt.
Now, setting the initial total momentum equal to the final total momentum and solving for the truck's final velocity Vt yields:
24200 kg·m/s = -12100 kg·m/s + 2.3 × 103 kg × Vt
Vt = (24200 kg·m/s + 12100 kg·m/s) / 2.3 × 103 kg
Vt = 36300 kg·m/s / 2300 kg = 15.78 m/s (approximately)
Therefore, the correct answer is C. +15.7 meters/second.