Gravity is really important for how projectiles move through the air.

When an object is launched, gravity is the main force pulling it down toward the Earth. This pull happens at a steady rate of about 9.81 meters per second squared.

While gravity pulls the projectile down, it does not change how fast the projectile moves sideways (if we ignore air resistance).

Because of this, the path that the projectile follows looks like a curved shape called a parabola. Here are a few key parts to understand:

1. Vertical Motion:

   • We can describe how high the projectile goes (this is called vertical position, or $y$) using this equation: $y = v_{0y}t - \frac{1}{2}gt^2$ In this equation, $v_{0y}$ is the starting speed going up, $g$ is how fast gravity pulls down, and $t$ is the time in seconds.

2. Horizontal Motion:

   • To figure out how far the projectile goes sideways (called horizontal position or $x$), we use: $x = v_{0x}t$ Here, $v_{0x}$ is the starting sideways speed, which stays the same throughout the motion.

3. Combined Motion:

   • We can look at the full path of the projectile by combining its upward and sideways motion. The equation that shows this path is: $y = \tan(\theta)x - \frac{g}{2(v_0 \cos \theta)^2}x^2$ Here, $\theta$ is the angle at which the projectile was launched, and $v_0$ is the initial speed.

The way the upward and sideways motions work together shows how gravity impacts the time the projectile stays in the air, its highest point, and how far it travels:

• Time of Flight: To find out how long the projectile is in the air (called time of flight, or $T$), we can use this formula: $T = \frac{2v_{0y}}{g}$

• Maximum Height: To figure out the highest point (maximum height, or $H$), we set the upward speed to zero and use: $H = \frac{(v_{0y})^2}{2g}$

• Range: To know how far it goes sideways (range, or $R$), we can use: $R = v_{0x}T = v_0 \cos(\theta) \cdot \frac{2v_{0y}}{g}$

In summary, gravity doesn’t just pull the projectile down. It also shapes how the projectile moves, creating a predictable curved path (parabola) known as projectile motion, which we can understand through simple equations.