Question

A ball is dropped from a cliff and falls a distance of 20 m to the ground. Determine the velocity it hits the ground at and the time for the ball to fall.

A.v = -10 m/s, t = 2 s
B.v = 20 m/s, t = 4 s
C.v = -20 m/s, t = 2 s
D.v = 10 m/s, t = 2 s

Answer 1

The ball hits the ground with a velocity of 19.6 m/s and it takes approximately 2.02 seconds for the ball to fall.

Step-by-step explanation:

To determine the velocity the ball hits the ground at, we can use the equation v = gt, where g is the acceleration due to gravity, approximately 9.8 m/s². Since the ball falls for 2 seconds, the velocity is given by v = 9.8 m/s² * 2 s = 19.6 m/s. Therefore, the ball hits the ground with a velocity of 19.6 m/s.

To determine the time it takes for the ball to fall, we can use the equation h = (1/2)gt², where h is the height and t is the time. Rearranging the equation, we have t = √(2h/g). Substituting the given height of 20 m, the time is t = √(2 * 20 m / 9.8 m/s²) = √4.08 s ≈ 2.02 s. Therefore, the time for the ball to fall is approximately 2.02 seconds.

Answer 2

Use the kinematic equation: d = vi • t + ½ • a • t^2
20=0(t)+(0.5)(9.8)(t^2)
20=4.9(t^2)
t=2.02seconds
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Final Velocity=Initial Velocity +at^2
Vf=(9.8)(2.02^2)
Vf=19.796