Question

A ball initially at rest is dropped from a window 24.3 m off the ground. How long does it take for the ball to reach the ground?

Answer 1

The ball takes 2.23 seconds to reach the ground

Step-by-step explanation:

Free Fall Motion

A free-falling object falls under the influence of gravity only. An object being acted upon only by the force of gravity is said to be in a state of free fall. Free-falling objects do not have air resistance.

If an object is dropped from rest in a free-falling motion, it falls with a constant acceleration called the acceleration of gravity, which value is
`g = 9.8 m/s^2`.

The distance traveled by a dropped object is:

`\displaystyle y=(gt^2)/(2)`

Knowing the height h from which the object was dropped, we can find the time it takes fo hit the ground:

`\displaystyle t=\sqrt{(2h)/(g)}`

Since y=24.3 m:

`\displaystyle t=\sqrt{(2\cdot 24.3)/(9.8)}`

t=2.23 seconds

The ball takes 2.23 seconds to reach the ground