Final answer:
In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision. Using the principle of conservation of momentum, we can calculate the velocity of car A after the collision. Plugging in the given values, the velocity of car A after the collision is 3.73 m/s.
Step-by-step explanation:
In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision. To find the velocity of car A after the collision, we can use the principle of conservation of momentum:
Calculate the initial momentum of car A: pAi = massA * velocityAi
Calculate the initial momentum of car B: pBi = massB * velocityBiCalculate the total initial momentum: ptotal_i = pAi + pBiCalculate the final momentum of car A: pAf = ptotal_i - pBiCalculate the final velocity of car A: velocityAf = pAf / massA
Plugging in the values, we get:
pAi = (296 kg)(3.74 m/s) = 1104.04 kg*m/s
pBi = (222 kg)(1.85 m/s) = 410.7 kg*m/s
ptotal_i = 1104.04 kg*m/s + 410.7 kg*m/s = 1514.74 kg*m/s
pAf = 1514.74 kg*m/s - 410.7 kg*m/s = 1104.04 kg*m/s
velocityAf = 1104.04 kg*m/s / 296 kg = 3.73 m/s
Therefore, the velocity of car A after the collision is 3.73 m/s.