Final answer:
The speed of the ball can be determined using the equation v = ω√(A² - x²), where v is the velocity, ω is the angular frequency, A is the amplitude, and x is the displacement. By substituting the given values into the equation, we find that the speed of the ball is approximately 3.25 m/s.
Step-by-step explanation:
The speed of the ball can be determined using the equation:
v = ω√(A² - x²)
where v is the velocity, ω is the angular frequency, A is the amplitude, and x is the displacement.
Given that the ball's velocity is 21.46 cm/s and its displacement is -14.60 cm, we can substitute these values into the equation to solve for the speed.
v = ω√(A² - x²)
21.46 = ω√((0.2146)² - (-0.146)²)
21.46 = ω√(0.0462 - 0.0213)
21.46 = ω√0.0249
ω = 21.46 / √0.0249
ω ≈ 15.16
The speed of the ball is equal to the product of the angular frequency and the amplitude:
Speed = ω * A
Speed = 15.16 * 0.2146
Speed ≈ 3.25 m/s