Calculating Speed in Free Fall

This problem involves calculating the final speed of an object undergoing free fall under gravity. We are given the initial state (at rest), the height from which it is dropped, and the acceleration due to gravity.

Physics Principles Applied

We can use the principles of kinematics to solve this problem. The relevant equation that connects final velocity ($v$), initial velocity ($u$), acceleration ($a$), and displacement ($s$ or $h$ in this case) is:

$ v^2 = u^2 + 2as $

In this specific scenario:

• Initial velocity, $u = 0$ m/s (since the ball is dropped from rest).
• Acceleration, $a = g = 10$ m/s$^2$ (acceleration due to gravity).
• Displacement (height), $h = 20$ m.

Step-by-Step Calculation

1. Identify Given Values:

   • Initial velocity ($u$) = 0 m/s
   • Height ($h$) = 20 m
   • Acceleration due to gravity ($g$) = 10 m/s$^2$

2. Select the Appropriate Kinematic Equation:

   The equation $v^2 = u^2 + 2gh$ relates the variables involved.

3. Substitute Values and Calculate:

   Substitute the known values into the equation:

   $ v^2 = (0 \text{ m/s})^2 + 2 \times (10 \text{ m/s}^2) \times (20 \text{ m}) $

   $ v^2 = 0 + 400 \text{ m}^2/\text{s}^2 $

   $ v^2 = 400 \text{ m}^2/\text{s}^2 $

4. Find the Final Speed:

   Take the square root of both sides to find $v$:

   $ v = \sqrt{400 \text{ m}^2/\text{s}^2} $

   $ v = 20 \text{ m/s} $

The speed with which the ball hits the ground is 20 m/s.