Free fall and projectiles (as framed)

Imagine you're at a super tall building and you drop a tiny pebble. What happens? It falls straight down, right? That's free fall! It means an object is only being pulled by gravity (the invisible force that pulls everything towards the Earth's center). We usually ignore air resistance for simplicity, like imagining the pebble is falling in a giant vacuum.

Now, what if you throw the pebble forward from that same building? It doesn't just fall straight down; it flies forward and falls down at the same time, making a curved path. This curved path is called projectile motion. Think of it like a basketball shot: the ball goes up, then forward, then down, all because of that initial push and gravity's constant pull.

Here's the cool part:

• Free fall is motion only in the up-and-down direction (vertical). Gravity makes things speed up as they fall.
• Projectile motion is motion in two directions at once: up-and-down (vertical) and side-to-side (horizontal). The horizontal motion is usually steady, while the vertical motion is affected by gravity, just like free fall.

Let's think about a cannon firing a cannonball. This is a classic example of projectile motion.

1. The Launch: When the cannon fires, it gives the cannonball a big push, sending it flying forward and usually a bit upwards. This is its initial velocity (starting speed and direction).
2. The Journey: As the cannonball flies through the air, two things are happening at the same time:
   • Horizontal Motion: It keeps moving forward at a pretty steady speed (if we ignore air pushing against it). There's no force pushing it faster forward once it leaves the cannon, and no force slowing it down horizontally (again, ignoring air resistance).
   • Vertical Motion: Gravity is constantly pulling it downwards. So, even though it might be going up at first, gravity slows its upward climb, stops it at the very top of its path, and then pulls it faster and faster downwards.
3. The Landing: Eventually, gravity wins, and the cannonball hits the ground. The path it took was a beautiful curve, a parabola, because of the combination of its steady forward motion and its gravity-affected up-and-down motion.

To understand how objects move in free fall or as projectiles, we break their motion into two separate, easier-to-handle parts:

1. Separate the Directions: Imagine a magical wall that splits the motion into a horizontal (sideways) part and a vertical (up-and-down) part. These two parts happen independently, meaning what happens horizontally doesn't directly mess with what happens vertically.
2. Analyze Horizontal Motion: For the horizontal part, if we ignore air resistance, there are no forces pushing or pulling the object sideways. This means its horizontal velocity (speed sideways) stays constant – it doesn't speed up or slow down horizontally.
3. Analyze Vertical Motion: For the vertical part, gravity is the boss! Gravity is always pulling the object downwards, causing it to accelerate (change its speed) downwards at a constant rate, which we call 'g' (about 9.8 m/s² on Earth).
4. Use Kinematic Equations: We use special math tools called kinematic equations (like formulas for distance, speed, and time) for each direction separately. For horizontal, we often use distance = speed × time. For vertical, we use equations that include acceleration due to gravity.
5. Connect with Time: The only thing that links the horizontal and vertical motions together is time. The object spends the same amount of time traveling horizontally as it does traveling vertically.
6. Put it Back Together: Once you've figured out what happened in each direction, you can combine them to describe the object's full path and where it ends up.