A cue stick has a mass of 0.5 kg. The cue stick hits a ball with a mass of 0.2 kg at a velocity of 2.5 m/s. What is the velocity of the ball after it is hit? (1 point)
6.3 m/s
8.3 m/s
O 2.5 m/s
3.6 m/s/
To find the velocity of the ball after it is hit, we can use the law of conservation of momentum. According to this law, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is calculated by multiplying its mass by its velocity.
The momentum before the collision is the mass of the cue stick (0.5 kg) multiplied by its velocity (2.5 m/s), which is equal to 1.25 kg·m/s.
The momentum after the collision is the sum of the momenta of the ball and the cue stick. Let's assume the velocity of the ball after the collision is v.
Therefore, the momentum of the ball after the collision is the mass of the ball (0.2 kg) multiplied by its velocity (v), which is equal to 0.2v kg·m/s.
The total momentum after the collision is 1.25 kg·m/s (from before the collision) + 0.2v kg·m/s (from the ball after the collision).
According to the law of conservation of momentum, the total momentum before and after the collision is the same. Therefore:
1.25 + 0.2v = 0.5 × v'
Simplifying the equation:
1.25 + 0.2v = 0.5v'
1.25 = 0.5v' - 0.2v
1.25 = 0.3v'
Dividing both sides of the equation by 0.3:
v' = 1.25 / 0.3
v' = 4.17 m/s
Therefore, the velocity of the ball after it is hit is approximately 4.17 m/s.