Final answer:
To find the final velocity of car 2, we can use the law of conservation of momentum. Applying this law to the given scenario, we found that the final velocity of car 2 is 31.94 m/s
Step-by-step explanation:
To find the final velocity of car 2, we can use the law of conservation of momentum. The law of conservation of momentum states that the total momentum before a collision is equal to the total momentum after the collision, provided no external forces are acting on the system.
Applying this law to the given scenario, we can write:
Initial momentum of car 1 + Initial momentum of car 2 = Final momentum of car 1 + Final momentum of car 2
Now, let's calculate the initial momentum:
Initial momentum of car 1 = mass of car 1 x velocity of car 1 = 19.5 kg x 16.1 m/s
Initial momentum of car 2 = mass of car 2 x velocity of car 2 = 7.7 kg x 0 m/s (since car 2 is stationary)
After the collision, car 1 has a final velocity of 3.5 m/s. Therefore, the final momentum of car 1 = mass of car 1 x final velocity of car 1 = 19.5 kg x 3.5 m/s
Let's substitute the values into the equation:
19.5 kg x 16.1 m/s + 7.7 kg x 0 m/s = 19.5 kg x 3.5 m/s + Final momentum of car 2
Simplifying the equation, we get:
Final momentum of car 2 = 19.5 kg x 16.1 m/s - 19.5 kg x 3.5 m/s = 19.5 kg x (16.1 m/s - 3.5 m/s)
Final momentum of car 2 = 19.5 kg x 12.6 m/s
Finally, to find the final velocity of car 2, we can divide the final momentum by the mass of car 2:
Final velocity of car 2 = Final momentum of car 2 / mass of car 2 = (19.5 kg x 12.6 m/s) / 7.7 kg
Calculating the value, we get:
Final velocity of car 2 = 31.94 m/s