Question

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Question:
An aerodynamic object of negligible air resistance is dropped from the top ledge of a tall building and falls to the ground. If the object fell 1/4 of the buildings height in the last second of flight, how tall is the building? * the acceleration of this object is due to gravity*

Answer 1

To find the height of the building, we apply kinematic formulas for free-fall, considering the distance covered in the last second and the acceleration due to gravity of 9.80 m/s², resulting in a building height of 19.6 meters.

Step-by-step explanation:

Finding the Height of a Building in a Free-Fall Scenario

When solving problems related to free-fall and the acceleration due to gravity, we use the average acceleration on Earth, which is 9.80 m/s². For an object falling the last quarter of the building's height in the last second, we can set up an equation using the kinematic formula for distance covered in free-fall: d = vi*t + (1/2)*g*t², where d is the distance, vi is the initial velocity (zero in this case), g is the acceleration due to gravity, and t is the time in seconds. Since the object fell for the last second, we can assume that it covered the last quarter of the distance in this time, thus t = 1 s and vi = 0 m/s. It is also known that the distance covered was h/4, where h is the total height of the building.

By plugging in the known values into the kinematic formula:

• 
  
• h/4 = 0*1 + (1/2)*9.80*1²
• 
  
• h/4 = 4.9

Thus, the height of the building, h, equals 19.6 meters.