Final answer:
The final velocity of the first 2.0 kg object after a one-dimensional elastic collision is 1.0 m/s in the positive x-direction, determined by applying the conservation of momentum.
Step-by-step explanation:
When dealing with a one-dimensional collision problem in physics, particularly an elastic collision, we apply the conservation of momentum and the conservation of kinetic energy principles. Since both objects involved are of equal mass (2.0 kg) and we are given the final velocity of the second object, we can solve for the final velocity of the first object after the collision.
To find the magnitude and direction of the velocity of the first 2.0 kg object after the collision, we use the conservation of momentum:
- Initial momentum = final momentum
- m1v1 + m2v2 = m1v'1 + m2v'2
Plugging the values into the equation, we get:
- (2.0 kg)(4.0 m/s) + (2.0 kg)(-3.0 m/s) = (2.0 kg)v'1 + (2.0 kg)(4.0 m/s)
- 8 kg·m/s - 6 kg·m/s = 2.0 kg·v'1 + 8 kg·m/s
- 2 kg·m/s = 2.0 kg·v'1
Dividing both sides of the equation by the mass of the first object (2.0 kg), we find that the final velocity of the first object v'1 = 1.0 m/s in the positive x-direction after the collision.