Answer :
Sure, let's work through the solution step by step to determine how long it would take an apple falling from a height of 4.00 meters to reach the ground.
First, we need to use the formula for the time of free fall. The formula that relates the height, gravitational acceleration, and time is:
[tex]\[ t = \sqrt{\frac{2h}{g}} \][/tex]
where:
- [tex]\( h \)[/tex] is the height from which the object is falling (in meters),
- [tex]\( g \)[/tex] is the acceleration due to gravity (in meters per second squared),
- [tex]\( t \)[/tex] is the time of free fall (in seconds).
Given:
- The height [tex]\( h = 4.00 \)[/tex] meters,
- The gravitational acceleration [tex]\( g = 9.8 \ \text{m/s}^2 \)[/tex].
Now substitute the given values into the formula:
[tex]\[ t = \sqrt{\frac{2 \times 4.00}{9.8}} \][/tex]
[tex]\[ t = \sqrt{\frac{8.00}{9.8}} \][/tex]
[tex]\[ t = \sqrt{0.8163265306} \][/tex]
[tex]\[ t \approx 0.903 \ \text{seconds} \][/tex]
So, the correct time taken for the apple to reach the ground is approximately 0.903 seconds.
Now, let’s compare this to the given options:
- A. 0.90 seconds
- B. 1.0 seconds
- C. 1.53 seconds
- D. 2.3 seconds
The closest and most accurate answer is:
A. 0.90 seconds
Therefore, the correct answer is 0.90 seconds (option A).
First, we need to use the formula for the time of free fall. The formula that relates the height, gravitational acceleration, and time is:
[tex]\[ t = \sqrt{\frac{2h}{g}} \][/tex]
where:
- [tex]\( h \)[/tex] is the height from which the object is falling (in meters),
- [tex]\( g \)[/tex] is the acceleration due to gravity (in meters per second squared),
- [tex]\( t \)[/tex] is the time of free fall (in seconds).
Given:
- The height [tex]\( h = 4.00 \)[/tex] meters,
- The gravitational acceleration [tex]\( g = 9.8 \ \text{m/s}^2 \)[/tex].
Now substitute the given values into the formula:
[tex]\[ t = \sqrt{\frac{2 \times 4.00}{9.8}} \][/tex]
[tex]\[ t = \sqrt{\frac{8.00}{9.8}} \][/tex]
[tex]\[ t = \sqrt{0.8163265306} \][/tex]
[tex]\[ t \approx 0.903 \ \text{seconds} \][/tex]
So, the correct time taken for the apple to reach the ground is approximately 0.903 seconds.
Now, let’s compare this to the given options:
- A. 0.90 seconds
- B. 1.0 seconds
- C. 1.53 seconds
- D. 2.3 seconds
The closest and most accurate answer is:
A. 0.90 seconds
Therefore, the correct answer is 0.90 seconds (option A).
