To calculate how long it takes for a ball to fall to the ground from a height of 20 meters (assuming no air resistance), you should use the following equation:
[tex]\[ \Delta t = \sqrt{\frac{2 \Delta d}{a}} \][/tex]
Here's a detailed step-by-step solution:
1. Identify the Known Variables:
- The height from which the ball falls, [tex]\( \Delta d = 20 \)[/tex] meters.
- The acceleration due to gravity, [tex]\( a = 9.8 \)[/tex] m/s².
2. Select the Correct Equation:
- We need to find the time [tex]\( \Delta t \)[/tex]. The appropriate kinematic equation for this is [tex]\( \Delta t = \sqrt{\frac{2 \Delta d}{a}} \)[/tex].
3. Plug the Known Values into the Equation:
Substitute [tex]\( \Delta d = 20 \)[/tex] meters and [tex]\( a = 9.8 \)[/tex] m/s² into the equation:
[tex]\[ \Delta t = \sqrt{\frac{2 \times 20 \, \text{m}}{9.8 \, \text{m/s}^2}} \][/tex]
4. Simplify the Equation:
First, calculate the numerator:
[tex]\[ 2 \times 20 = 40 \][/tex]
Then, divide by the acceleration due to gravity:
[tex]\[ \frac{40}{9.8} \approx 4.08 \][/tex]
Finally, take the square root of the result:
[tex]\[ \sqrt{4.08} \approx 2.02 \][/tex]
Therefore, the time it takes for the ball to fall to the ground from a height of 20 meters is approximately [tex]\( \Delta t \approx 2.02 \)[/tex] seconds.
So, the correct equation to use is:
B. [tex]\(\Delta t = \sqrt{\frac{2 \Delta d}{a}}\)[/tex]
