Final answer:
The velocity of ball 2 after the impact is approximately -1.93 m/s in the opposite direction of ball 1's initial velocity.
Step-by-step explanation:
To find the velocity of ball 2 after the impact, we can use the principle of conservation of momentum. Since the two balls have equal masses and no external forces are acting on them, the total momentum before the impact is equal to the total momentum after the impact.
Before the impact, ball 1 is moving horizontally at 3.00 m/s. After the impact, it is moving at 0.50 m/s at 50° from the original direction. To find the velocity of ball 2 after the impact, we can separate the velocity of ball 1 into its horizontal and vertical components.
The horizontal component of ball 1's velocity is given by: 3.00 m/s * cos(50°) = 1.93 m/s
The vertical component of ball 1's velocity is given by: 3.00 m/s * sin(50°) = 2.30 m/s
Since ball 2 is at rest, its initial velocity is 0 m/s.
To find the final velocity of ball 2, we can use the principle of conservation of momentum:
Initial momentum = final momentum
Momentum of ball 1 + Momentum of ball 2 = 0
Using the momentum equation: (mass of ball 1 * velocity of ball 1) + (mass of ball 2 * velocity of ball 2) = 0
Plugging in the values:
(0.300 kg * 1.93 m/s) + (0.300 kg * velocity of ball 2) = 0
Simplifying the equation: 0.579 kg·m/s + 0.300 kg·velocity of ball 2 = 0
Solving for the velocity of ball 2: velocity of ball 2 = -0.579 kg·m/s ÷ 0.300 kg ≈ -1.93 m/s
Therefore, the velocity of ball 2 after the impact is approximately -1.93 m/s in the opposite direction of ball 1's initial velocity.