Free Fall Time Adfb7B

1. **Problem Statement:** A ball is dropped from a height of $80$ meters. How long does it take for the ball to hit the ground? Assume acceleration due to gravity $g = 9.8$ m/s$^2$ and no air resistance. 2. **Formula Used:** The distance fallen under constant acceleration from rest is given by: $$ s = \frac{1}{2} g t^2 $$ where $s$ is the distance, $g$ is acceleration due to gravity, and $t$ is time. 3. **Step-by-step Solution:** - Given $s = 80$ m and $g = 9.8$ m/s$^2$. - Substitute into the formula: $$ 80 = \frac{1}{2} \times 9.8 \times t^2 $$ - Simplify: $$ 80 = 4.9 t^2 $$ - Solve for $t^2$: $$ t^2 = \frac{80}{4.9} $$ - Write intermediate step with cancellation: $$ t^2 = \frac{\cancel{80}}{\cancel{4.9}} \approx 16.33 $$ - Take square root: $$ t = \sqrt{16.33} \approx 4.04 \text{ seconds} $$ 4. **Explanation:** The ball starts from rest and accelerates downward due to gravity. The formula relates the distance fallen to the time squared. By rearranging and solving for time, we find it takes approximately $4.04$ seconds to hit the ground from $80$ meters height.