Projectile Range vs. Projectile Displacement: Key Differences

Question

Hey everyone! 👋 I'm a student just like you, and I always got confused between projectile range and projectile displacement in physics. It's like, aren't they the same thing? 🤔 Turns out, they're not! Let's break it down in simple terms so we can all ace our next physics test! 💯

dawnlee2004 · Accepted Answer

📚 Projectile Range vs. Projectile Displacement: Understanding the Key Differences

In physics, especially when studying projectile motion, it's crucial to understand the difference between projectile range and projectile displacement. While both relate to the distance a projectile covers, they represent different aspects of its motion.

🎯 Definition of Projectile Range
Projectile range refers to the horizontal distance a projectile travels before landing back at the same vertical height from which it was launched. It's a scalar quantity, meaning it only has magnitude and no direction. We often assume a flat surface for simplicity.

📏 Definition of Projectile Displacement
Projectile displacement, on the other hand, is a vector quantity that represents the change in position of the projectile from its starting point to its ending point. It includes both magnitude (the straight-line distance between the initial and final positions) and direction.

Feature
            Projectile Range
            Projectile Displacement

Definition
            Horizontal distance traveled before landing at the same vertical height.
            Change in position from start to end, including both distance and direction.

Type of Quantity
            Scalar (magnitude only)
            Vector (magnitude and direction)

Formula (Ideal Case)
            $R = \frac{v^2 \sin(2	heta)}{g}$ (where $v$ is initial velocity, $	heta$ is launch angle, and $g$ is acceleration due to gravity)
            $\Delta r = r_{final} - r_{initial}$ (where $r$ represents the position vector)

Vertical Consideration
            Assumes landing at the same vertical height as the launch point.
            Considers the vertical change in position.

Example
            A ball thrown across a field travels 50 meters horizontally.
            A bird flies 30 meters East and 10 meters up.

✨ Key Takeaways

📏 Range is Distance: Projectile range focuses solely on the horizontal distance covered.
    🧭 Displacement is Directional: Projectile displacement considers both horizontal and vertical changes in position, providing a direction.
    📐 Ideal Range Formula: The range formula $R = \frac{v^2 \sin(2	heta)}{g}$ is only valid when the projectile lands at the same vertical height as its launch point.
    📍 Displacement Vector: Displacement is a vector pointing from the starting point to the ending point, regardless of the path taken.

Projectile Range vs. Projectile Displacement: Key Differences

1 Answers

📚 Projectile Range vs. Projectile Displacement: Understanding the Key Differences

🎯 Definition of Projectile Range

📏 Definition of Projectile Displacement

✨ Key Takeaways

Join the discussion

Feature	Projectile Range	Projectile Displacement
Definition	Horizontal distance traveled before landing at the same vertical height.	Change in position from start to end, including both distance and direction.
Type of Quantity	Scalar (magnitude only)	Vector (magnitude and direction)
Formula (Ideal Case)	$R = \frac{v^2 \sin(2\theta)}{g}$ (where $v$ is initial velocity, $\theta$ is launch angle, and $g$ is acceleration due to gravity)	$\Delta r = r_{final} - r_{initial}$ (where $r$ represents the position vector)
Vertical Consideration	Assumes landing at the same vertical height as the launch point.	Considers the vertical change in position.
Example	A ball thrown across a field travels 50 meters horizontally.	A bird flies 30 meters East and 10 meters up.