Simulation · Kinematics

Projectile motion

Explore how horizontal and vertical velocity components produce an ideal parabolic trajectory under uniform gravity.

Physical model

Two components, one trajectory

The particle starts at x₀ = 0 and height y₀. With no air resistance, horizontal motion is uniform and vertical motion has constant acceleration ay = −g. Flight ends at the first contact with the ground, y = 0.

x(t)=vx0ty(t)=y0+vy0t−12gt2vx(t)=vx0vy(t)=vy0−gt

vx₀ = v₀ cos θ · vy₀ = v₀ sin θ

2D Canvas

Trajectory in the Cartesian plane

The geometry uses +y upward; vectors use independent visual scales.

  • Complete trajectory
  • Current position

The Canvas represents the ground, axes, complete trajectory, and instantaneous position. Equivalent numerical readings follow the scene.

Vectors are scaled for easier comparison; their pixel length does not use the spatial scale of the axes.

Text alternative to the Canvas

Physical state

Instant t
0 s
Horizontal position x
0 m
Vertical position y
0 m
Horizontal velocity vx
14.14 m/s
Vertical velocity vy
14.14 m/s
Speed |v|
20 m/s
Horizontal acceleration ax
0 m/s²
Vertical acceleration ay
-9.8 m/s²
Flight time
2.89 s
Range
40.82 m
Maximum height
10.2 m

Physical time

Playback

Paused

Exploration guide

What to observe

  1. 01

    Keep v₀ fixed and compare 25°, 45°, and 70° while observing range and flight time.

  2. 02

    Verify that vx remains constant while vy changes linearly under gravity.

  3. 03

    At the highest point, vy is zero, but vx generally remains nonzero.

  4. 04

    Compare a horizontal launch from a height with launches from ground level.

  5. 05

    Change g while holding all other conditions fixed and analyze how range and maximum height vary.

Scope

Model limits

The projectile is a point particle under uniform gravity. There is no air, wind, rotation, bounce, or Earth curvature. The classical maximum-range result at 45° applies only when launch and landing heights are equal, with uniform gravity and no air resistance. Vector lengths use a visual scale different from the plane's spatial scale.