A steel ball is dropped from rest from the roof of a building. An observer standing behind a window that is part way down the building 120 cm high notes the ball takes 0.125 s to fall from the top to the bottom of the window. The ball continues to fall, makes an elastic collision with the sidewalk and rebounds appearing at the bottom of the window 2.0 s after passing it on the way down. How tall is the building?

Question

A steel ball is dropped from rest from the roof of a building. An observer standing behind a window that is part way down the building 120 cm high notes the ball takes 0.125 s to fall from the top to the bottom of the window. The ball continues to fall, makes an elastic collision with the sidewalk and rebounds appearing at the bottom of the window 2.0 s after passing it on the way down. How tall is the building?

Answer 1

To find the height of the building, we can use the equations of motion and the concept of free fall. Here's how we can calculate it:

1. First, let's calculate the time it takes for the ball to fall from the roof to the window. Since the observer notes that it takes 0.125 seconds to fall from the top to the bottom of the window, we can assume the window is halfway down the building. Therefore, the time it takes for the ball to reach the window is half of 0.125 seconds, which is 0.0625 seconds.

2. Now, let's calculate the time it takes for the ball to reach the sidewalk after rebounding. The total time for this is given as 2.0 seconds.

3. We know that the time it takes for the ball to reach the window is 0.0625 seconds. So, the time it takes for the ball to reach the sidewalk after rebounding is the total time (2.0 seconds) minus the time to reach the window (0.0625 seconds), which equals 1.9375 seconds.

4. Now, let's use the equation of motion for free fall: h = 1/2 * g * t^2, where h is the height, g is the acceleration due to gravity, and t is the time.

5. Since the ball undergoes free fall, the acceleration due to gravity can be approximated as 9.8 m/s^2.

6. Let's calculate the height from the roof to the window by plugging in the values: h = 1/2 * 9.8 * (0.0625)^2 = 0.019140625 meters.

7. To find the total height of the building, we need to add the height from the window to the sidewalk and the height from the roof to the window: total height = 120 cm + 0.019140625 meters = 120.019140625 cm.

8. Therefore, the height of the building is approximately 120.02 cm or 1.20 meters.

Therefore, the height of the building is approximately 1.20 meters.