If we drop a feather and a stone of the same height, we observe that the stone will reach the ground first.

So we think the heavier the body, the faster it will fall. However, if we place the stone and quill in an airless tube (vacuum), we will notice that both objects take the same time to fall.

Thus, we conclude that if we neglect air resistance, all bodies, regardless of mass or shape, will fall with a constant acceleration: the acceleration of gravity.

When a body is thrown near the Earth, it is then subject to gravity, which is always oriented vertically toward the center of the planet.

The value of gravity (g) varies according to the latitude and altitude of the site, but during short-term phenomena it is taken as constant and its mean value at sea level is:

**g = 9.80665m / s²**

However, as a good rounding, we can use without much loss in values:

**g = 10m / s²**

## Vertical release

A pitch of a body with initial velocity in the vertical direction is called the Vertical Throw.

Its trajectory is rectilinear and vertical, and due to gravity, the movement is classified as Uniformly Varied.

The functions governing the vertical throw, therefore, are the same as those of uniformly varied movement, revised with the vertical frame (**H**), where it was previously horizontal (**s**) and with acceleration of gravity (**g**).

Being that **g** is positive or negative depending on the direction of movement:

### Vertical Launch Up

### G is negative

Since gravity always points downwards, when we throw something upwards, the movement will be negatively accelerated until it stops at a point, which we call *Maximum height.*

### Vertical Flipping Down

### G is positive

In vertical downward casting, both gravity and displacement point downward. Therefore, the movement is positively accelerated. It is also named after *free fall.*

Example

A soccer ball is kicked upwards at a speed of 20m / s.

(a) Calculate how long it will take the ball to return to the ground.

(b) What is the maximum height reached by the ball? Given g = 10m / s².

*(The)*

*In this example, the movement is a combination of a vertical upward throw + a vertical downward throw (which in this case can also be called free fall). So, the most appropriate is to calculate by parts:*

*Upward movement:*

*Downward motion*:

*Since we are not considering air resistance, the final velocity will be equal to the speed with which the ball was thrown.*

* *

*We observe, then, that in this situation, where the air resistance is neglected, the rise time is the same as the decide time.*

**(B)**

*Knowing the rise time and launch speed, we can use the time offset function, or use the Torricelli equation.*

*Remember we are only considering the climb, so t = 2s*

*or*