a heavy object is dropped from the top of a 25 m tall building and it reaches the ground in 2.26 seconds determine the acceleration due to gravity how far did the object fall during the first second how far did the object fall during the 2nd second
hf=hi+1/2 gt^2
hf=0 hi=25 t=2.26
g=-25*2/2.26^2
To determine the acceleration due to gravity, we can use the equation for free-falling motion:
d = 1/2 * g * t^2,
where:
- d is the distance fallen,
- g is the acceleration due to gravity, and
- t is the time taken.
Given that the object falls from a height of 25 meters and takes 2.26 seconds, we can use this equation to find the acceleration due to gravity.
25 = 1/2 * g * (2.26)^2.
To solve for g, we can rearrange the equation:
g = (2 * d) / t^2.
Plugging in the values, we get:
g = (2 * 25) / (2.26)^2 ≈ 9.79 m/s^2.
So, the acceleration due to gravity is approximately 9.79 m/s^2.
Now, let's calculate how far the object fell during the first second and the second second.
During the first second (t = 1), we can use the same equation to find the distance fallen:
d1 = 1/2 * g * t^2 = 1/2 * 9.79 * 1^2 = 4.89 meters.
Therefore, during the first second, the object fell approximately 4.89 meters.
During the second second (t = 2), we can again use the same equation:
d2 = 1/2 * g * t^2 = 1/2 * 9.79 * 2^2 = 19.58 meters.
So, during the second second, the object fell approximately 19.58 meters.
To summarize:
- The acceleration due to gravity is approximately 9.79 m/s^2.
- The object fell approximately 4.89 meters during the first second.
- The object fell approximately 19.58 meters during the second second.