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Horizontal Projectile: Motion Independence Guide

PhysicsBeginnerReading time: 3 min

Overview

Through this experiment, you can intuitively explore the laws of horizontal projectile motion. Using stroboscopic animation, compare the trajectories of a horizontally projected ball with those of a free-falling ball and a ball in uniform rectilinear motion, giving you a deep understanding of the independent component motions in horizontal and vertical directions.

Background

In the 17th century, Galileo Galilei first detailed projectile motion in his work *Dialogues Concerning Two New Sciences*. He proposed that projectile motion could be decomposed into uniform motion in the horizontal direction and naturally accelerated motion (free fall) in the vertical direction. This discovery not only overturned Aristotle's old concepts but also laid the foundation for Newtonian mechanics. Understanding projectile motion is key to mastering curvilinear motion and the composition and decomposition of motions.

Key Concepts

Horizontal Projectile Motion

Trajectory:y=g2v02x2Trajectory: y = \frac{g}{2v_0^2}x^2

The motion of an object projected with a certain initial velocity in the horizontal direction, moving under the influence of gravity alone.

Principle of Independence of Motion

v⃗=v⃗x+v⃗y\vec{v} = \vec{v}_x + \vec{v}_y

When an object participates in several simultaneous motions, each component motion takes place independently without affecting the others. The actual motion is the vector sum of these component motions.

Free Fall Motion

h=12gt2h = \frac{1}{2}gt^2

The motion of an object falling from rest under the influence of gravity alone. The vertical component of horizontal projectile motion is free fall.

Uniform Rectilinear Motion

x=v0tx = v_0t

Motion with constant speed in a straight line. Since there is no force acting in the horizontal direction (ignoring air resistance), current projectile motion is uniform rectilinear in that direction.

Experiment Steps

  1. 1

    Observe Vertical Component

    Click “Start Experiment” to observe the Red Ball (Projectile) and Blue Ball (Free Fall). Is there any difference in their falling speed in the vertical direction? Do they hit the ground at the same time? What does this imply?
  2. 2

    Observe Horizontal Component

    Reset the experiment and click Start again. Focus on the Red Ball and Green Ball (Reference). Are their positions in the horizontal direction always aligned at any moment before the red ball hits the ground? What does this suggest about the horizontal law of projectile motion?
  3. 3

    Explore Initial Velocity

    Keep Height (h) constant and change Initial Velocity (v₀). Predict: When the initial velocity increases, will the flight time change? How will the horizontal range change? Verify your hypothesis with the simulation.
  4. 4

    Explore Height

    Keep Initial Velocity (v₀) constant and change Height (h). Does higher height lead to longer or shorter flight time? How does it affect the horizontal range?

Learning Outcomes

  • Understand that horizontal projectile motion can be decomposed into uniform rectilinear motion horizontally and free fall motion vertically.
  • Master the concept that flight time is determined solely by height and is independent of initial velocity.
  • Master the concept that horizontal range is determined by both initial velocity and height.
  • Experience the research method of “linearizing curves” and the idea of composition and decomposition of motion.

Real-world Applications

  • Relief Supply Drops: When airplanes drop relief supplies mid-air, they must calculate the drop point based on height and plane speed, as supplies follow a projectile path.
  • Sports: The trajectories of flat serves in tennis or volleyball, and horizontal batting in baseball, approximate projectile motion (ignoring air resistance).
  • Hydraulic Engineering: When water is discharged from dam spillways or horizontal fountain nozzles, the water stream follows a parabolic path. Design requires projectile laws to calculate the impact area.
  • Forensics: Inferring the initial position and velocity of a fallen object by analyzing its impact location and impact marks.

Common Misconceptions

Misconception
False belief that objects with higher initial velocity fall faster.
Correct
In reality, flight time depends only on height (t=2h/gt=\sqrt{2h/g}), regardless of horizontal initial velocity.
Misconception
False belief that the trajectory of projectile motion is a circular arc.
Correct
In reality, the trajectory is a parabola (y∝x2y \propto x^2).
Misconception
False belief that the object moves forward due to a lingering pushing force.
Correct
In reality, after leaving the hand, the object is only acted upon by gravity; horizontal motion is maintained by inertia.

Further Reading

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Now that you understand the basics, start the interactive experiment!

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