answer: the final speed of the 2 kg ball is 0.25 m/s.
Step-by-step explanation:
To solve this problem, we can use the law of conservation of momentum, which states that the total momentum of a system before a collision is equal to the total momentum after the collision.
The momentum of an object is defined as the product of its mass and velocity:
momentum = mass x velocity
So, the total momentum before the collision can be calculated as:
total momentum before = (mass of ball 1 x velocity of ball 1) + (mass of ball 2 x velocity of ball 2)
total momentum before = (2 kg x 3.5 m/s) + (3 kg x 2.5 m/s)
total momentum before = 7 kg m/s + 7.5 kg m/s
total momentum before = 14.5 kg m/s
After the collision, the 3 kg ball moves at 5.0 m/s in its original direction. Let's assume that the 2 kg ball moves at a final velocity of v.
Using the law of conservation of momentum, we can write:
total momentum after = (mass of ball 1 x final velocity of ball 1) + (mass of ball 2 x final velocity of ball 2)
total momentum after = (2 kg x v) + (3 kg x 5.0 m/s)
total momentum after = 2v kg m/s + 15 kg m/s
Since the total momentum before the collision is equal to the total momentum after the collision, we can set these two expressions equal to each other:
total momentum before = total momentum after
14.5 kg m/s = 2v kg m/s + 15 kg m/s
Solving for v, we get:
v = (14.5 kg m/s - 15 kg m/s) / 2 kg
v = -0.25 m/s
Since the final velocity cannot be negative, we know that the 2 kg ball is moving in the opposite direction after the collision. So, we can take the absolute value of v to find the final speed of the ball:
final speed = |v| = |-0.25 m/s| = 0.25 m/s
Therefore, the final speed of the 2 kg ball is 0.25 m/s.