A Ball Dropped from Hotel Balcony: How High Above the Ground?

The Ball Drop Scenario

A ball is dropped off the balcony of a hotel room and it takes 2.8 seconds to fall to the ground. The height of the ball above the ground is calculated to be 38.45 meters.

Calculating the Height of the Ball

First, we will calculate the velocity of the ball when it touches the ground by using the first equation of motion:

v = u + gt

Here, at the point of contact with the ground:

Initial velocity (u) = 0 m/s (as the ball is dropped)

Time taken (t) = 2.8 seconds

Acceleration due to gravity (g) = 9.81 m/s^2

Substitute these values into the equation:

v = 0 + 9.81 * 2.8

Therefore, the velocity of the ball when it touches the ground is approximately 27.468 m/s.

Next, we can calculate the height from the ground using the formula:

v = √(2gh)

Substitute the values:

27.468 = √(2 * 9.81 * h)

Solving for h:

h = 38.45 meters

Therefore, the height of the balcony above the ground is 38.45 meters.

How did we calculate the height of the ball dropped from the balcony of the hotel?

We calculated the height of the ball by first determining the velocity of the ball when it touches the ground using the equation of motion, and then using the calculated velocity to find the height from the ground with another formula involving acceleration due to gravity.