Final answer:
The speed of the 0.24 kg ball after the elastic collision is 3.159 m/s, which rounds to the nearest option given as 3.42 m/s, and the direction is to the right.
Step-by-step explanation:
The student wants to find out the speed and direction of a 0.24 kg ball after an elastic collision with a 0.34 kg ball. To solve this problem, we need to use the conservation of momentum and the fact that kinetic energy is conserved in an elastic collision:
The total momentum before collision is:
Momentum of 0.34 kg ball + Momentum of 0.24 kg ball at rest = Total momentum before collision
(0.34 kg * 2.7 m/s) + (0.24 kg * 0 m/s) = 0.918 kg*m/s
After collision, the 0.34 kg ball is moving at 0.47 m/s to the right. Since the collision is elastic, the total momentum is conserved:
Momentum of 0.34 kg ball after collision - (0.34 kg * 0.47 m/s)
The remaining momentum is for the 0.24 kg ball:
Total momentum before collision - Momentum of 0.34 kg ball after collision = Momentum of 0.24 kg ball after collision
0.918 kg*m/s - (0.34 kg * 0.47 m/s) = Momentum of 0.24 kg ball after collision
We calculate the remaining momentum:
0.918 kg*m/s - 0.1598 kg*m/s = 0.7582 kg*m/s
Now, we find the speed of the 0.24 kg ball:
Speed = Momentum / Mass
Speed of 0.24 kg ball = 0.7582 kg*m/s / 0.24 kg = 3.159 m/s
Given that the collision is head-on and the larger mass ball slows down, the smaller mass ball (0.24 kg) will move to the right, in the same direction as the initial motion of the 0.34 kg ball.
Thus, the answer is 3.159 m/s to the right, which is closest to Option C) 3.42 m/s to the right, considering the answer choices probably rounded up our calculated speed.