a student sees a ball fall from the third floor of a building and notes that it takes 2.50 s for the ball to fall the last half of the way to the ground. What is the height of the building?
how?
-160.35 m
To determine the height of the building, we can use the equations of motion and the concept of free fall.
When an object is in free fall near the surface of the Earth, the distance it falls is given by the equation:
h = 0.5 * g * t^2
Where:
- h is the height or distance fallen
- g is the acceleration due to gravity (approximately 9.8 m/s^2 near the surface of the Earth)
- t is the time it takes to fall
In this scenario, we know that it takes 2.50 seconds for the ball to fall the last half of the way to the ground. Let's call this time interval t_last.
We can use this information to find the total time it takes for the ball to fall from the top of the building to the ground. Since the ball falls the last half of the way in 2.50 seconds, the total time it takes for the ball to fall from the top to the ground is twice that, which is 5.00 seconds. Let's call this total time t_total.
Now, let's find the height of the building. We know that the distance fallen (h) is equal to the height of the building. Plugging in the values into the equation of motion:
h = 0.5 * g * t_total^2
Substituting g = 9.8 m/s^2 and t_total = 5.00 s:
h = 0.5 * 9.8 * (5.00)^2
Calculating:
h = 0.5 * 9.8 * 25
h = 122.5 m
Therefore, the height of the building is 122.5 meters.