Final answer:
To find the combined velocity of a 1000 kg car colliding with a 1500 kg stationary car and locking together, the conservation of momentum concept is applied. The combined velocity after the collision is calculated to be 5.64 m/s.
Step-by-step explanation:
The question involves the concept of conservation of momentum, which states that the total momentum of a closed system remains constant if no external forces act on it. To find the combined velocity of a 1000 kg car colliding with a 1500 kg stationary car and locking together, we use the formula:
Total momentum before collision = Total momentum after collision
Momentum of moving car = (mass of car) × (velocity of car) = 1000 kg × 14.1 m/s = 14100 kg·m/s.
The stationary car has zero momentum since its velocity is zero. After the collision, both cars move with the same velocity V.
Therefore, the total momentum after the collision is:
(total combined mass) × V = (1000 kg + 1500 kg) × V.
To find V, we set the total momentum before collision equal to the total momentum after collision:
14100 kg·m/s = (2500 kg) × V.
Solving for V gives:
V = 14100 kg·m/s ÷ 2500 kg = 5.64 m/s.
The combined velocity of the two locked cars immediately after the collision is 5.64 m/s.