Final answer:
Using the equations of motion for uniform acceleration, the final speed of a 2.0 kg ball that free falls from rest through a vertical displacement of -0.20 m, ignoring air resistance, is approximately 1.98 m/s.
Step-by-step explanation:
To determine the final speed of a 2.0 kg ball that free falls from rest through a vertical displacement of -0.20 m, we can use the equations of motion for uniformly accelerated motion without air resistance. The equation linking final velocity (v), initial velocity (v0), acceleration (a), and displacement (s) is: v^2 = v0^2 + 2as. In this case, the initial velocity is zero, acceleration is due to gravity (g = 9.8 m/s²), and the displacement is -0.20 m (sign indicates direction).
Substituting the values, we have:
v^2 = 0 + 2 (9.8 m/s²) (-0.20 m)
v^2 = -3.92 m²/s².
Since the final velocity cannot be negative, we take the positive square root of the absolute value:
v = √3.92 m²/s²
v ≈ 1.98 m/s. The final speed of the ball is approximately 1.98 m/s.