When an object is thrown or launched with an initial velocity at an angle to the horizontal, it experiences projectile motion, moving in a parabolic path due to the acceleration caused by gravity.

This motion can be seen when you throw a ball, shoot an arrow, or launch a rocket.

## Role of Gravity

Gravity is a force that pulls objects toward the Earth. It’s the same force that makes things fall when you drop them. Here’s how gravity affects the different parts of projectile motion:

## Vertical Motion

When you throw an object, it goes up into the air. Gravity starts to pull it down as soon as it leaves your hand.

As the object goes higher, gravity slows it down. Eventually, it stops going up and starts to fall back down.

The speed at which the object falls increases as it comes back down because gravity is pulling it faster and faster.

The vertical motion can be described by the equation:

\[ y(t) = v_{0y} t – \frac{1}{2} g t^2 \]

where \( y(t) \) is the vertical position at time \( t \), \( v_{0y} \) is the initial vertical velocity, and \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)).

## Horizontal Motion

Gravity does not affect the horizontal (sideways) motion of the object directly. If you ignore air resistance, the object moves horizontally at a constant speed.

However, because gravity is pulling the object downward, the path of the object will curve downward over time, making a parabolic (curved) shape.

The horizontal motion can be described by the equation:

\[ x(t) = v_{0x} t \]

where \( x(t) \) is the horizontal position at time \( t \), and \( v_{0x} \) is the initial horizontal velocity.

## Combined Effect

Imagine throwing a ball straight out in front of you:

It moves forward because you threw it (this is the horizontal motion).

At the same time, gravity pulls it downward (this is the vertical motion).

**The combination of these two motions—one horizontal and one vertical—creates the curved path we see in projectile motion.**

The overall path (trajectory) of the projectile is described by the equation:

\[ y(x) = x \tan(\theta) – \frac{g x^2}{2 v_{0}^2 \cos^2(\theta)} \]

where \( \theta \) is the launch angle, and \( v_{0} \) is the initial velocity.

## Summary

In summary, gravity is the reason why projectiles follow a curved path. It pulls the object downward, affecting the vertical motion, while the horizontal motion remains unaffected by gravity, creating the characteristic arc of projectile motion.