Calculating the Height of a Balcony Using Free-Fall Motion

Question:

You want to verify the height of a balcony. You drop something off of the balcony, and it takes 2.7 seconds to reach the ground. How high is the balcony?

Answer:

The height of the balcony is approximately 35.04 meters.

Explanation:

To calculate the height of the balcony, we can use the equation for free-fall motion. The equation is:

height = (1/2) * gravity * time^2

Given that it takes 2.7 seconds for an object to reach the ground, we need to know the value of gravity. On Earth, the value of gravity is approximately 9.8 m/s^2. Plugging in the values, we get:

height = (1/2) * 9.8 m/s^2 * (2.7 s)^2

Simplifying, we find that the height of the balcony is approximately 35.04 meters.