Final answer:
The two carts, after undergoing an inelastic collision on a frictionless surface, will have a final velocity of 2.75 m/s using the law of conservation of momentum to calculate the result.
Step-by-step explanation:
The question is about the final velocity of two colliding carts that stick together after an inelastic collision on a frictionless surface. To solve for the final velocity, the law of conservation of momentum can be applied. The combined momentum before the collision must equal the combined momentum after the collision, since there are no external forces acting on the carts. The initial momentum is the sum of the momentum of each cart (mass times velocity), and the final momentum is the combined mass times the final velocity.
The equation for conservation of momentum in this case is:
mAvA + mBvB = (mA+mB)vfinal
Plugging in the values from the question (3.00 kg * 4.00 m/s + 5.00 kg * 2.00 m/s), we calculate the final velocity:
vfinal = (3.00 kg * 4.00 m/s + 5.00 kg * 2.00 m/s) / (3.00 kg + 5.00 kg)
vfinal = (12 + 10) kg*m/s / 8.00 kg
vfinal = 22 kg*m/s / 8.00 kg
vfinal = 2.75 m/s
The colliding carts will have a final velocity of 2.75 m/s after the collision.