Final answer:
To determine the fall time for a ball from 20 meters, we use the free fall motion equation with a displacement of 20 m, initial velocity of 0, and gravitational acceleration of 9.8 m/s². The calculated time is approximately 2.02 seconds.
Step-by-step explanation:
To calculate the time it takes for a ball to fall from a height of 20 meters, we can use the basic equations of motion for objects in free fall. The formula to find the time (t) taken by an object dropped from rest (initial velocity u = 0) under the influence of gravity (g = 9.8 m/s2) is derived from the equation:
s = ut + 1/2 gt2
Where:
- s is the displacement, which is 20 m in this case,
- u is the initial velocity, which is 0 because the ball is released and not thrown,
- g is the acceleration due to gravity (approximately 9.8 m/s2 on Earth),
- t is the time.
By substituting the values into the formula, we get:
20 = 0 * t + 1/2 * 9.8 * t2
20 = 4.9 * t2
To find t, we divide both sides by 4.9,
t2 = 20 / 4.9
t2 = 4.08
And by taking the square root,
t = √4.08
t ≈ 2.02 s
Therefore, the time it takes for a ball to fall from a height of 20 meters is approximately 2.02 seconds.