Final answer:
The final speed of the two cars after the collision is v / (1 + 0.395) as a fraction of the initial speed v.
Step-by-step explanation:
In order to calculate the final velocity of the two cars after the collision, we need to use the principle of conservation of momentum.
Let's assume the initial velocity of the first car (car 1) is v. The initial velocity of the second car (car 2) is 0 since it is stationary.
According to the principle of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.
The total momentum is given by:
Total momentum before collision = Total momentum after collision
Since the two cars stick together after the collision and move off in the same direction as before, their final velocity will be the same. Let's call this final velocity V.
Using the principle of conservation of momentum, we can write:
mv + 0 = (m₁ + m₂)V
where m₁ is the mass of car 1, and m₂ is the mass of car 2.
Given that the second car is 39.5% as massive as the first car, we have:
m₂ = 0.395m₁
Substituting this into the equation:
mv = (m₁ + 0.395m₁)V
Simplifying the equation:
V = v / (1 + 0.395)
Therefore, the final speed of the two cars after the collision is v / (1 + 0.395) as a fraction of the initial speed v.