Ball Drop: Velocity and Time Calculation

A ball is dropped from a cliff and falls a distance of 20 m to the ground. Determine the velocity at which it hits the ground at and the time it took for the ball to fall. (where, g = 10 m/s^2) Group of answer choices

v = 10 m/s, t = 2 s

v = -20 m/s, t = 2 s

v = 20 m/s, t = 4 s

v = -10 m/s, t = 2 s

To solve this problem, we can use the equations of motion under constant acceleration due to gravity.

1. Finding the time of fall (t): We can use the equation for distance fallen under constant acceleration: [ d = \frac{1}{2} g t^2 ] where:

• (d = 20 , \text{m}) (the distance fallen),
• (g = 10 , \text{m/s}^2) (acceleration due to gravity).

Rearranging the equation to solve for (t): [ 20 = \frac{1}{2} \cdot 10 \cdot t^2 ] [ 20 = 5t^2 ] [ t^2 = \frac{20}{5} = 4 ] [ t = \sqrt{4} = 2 , \text{s} ]

2. Finding the final velocity (v): We can use the equation for final velocity under constant acceleration: [ v = g t ] Substituting the values we have: [ v = 10 \cdot 2 = 20 , \text{m/s} ]

Since the ball is falling downwards, we can consider the velocity to be negative in the context of direction: [ v = -20 , \text{m/s} ]

Thus, the final results are:

• The velocity at which it hits the ground is (v = -20 , \text{m/s}).
• The time it took for the ball to fall is (t = 2 , \text{s}).

The correct answer from the choices provided is: v = -20 m/s, t = 2 s.