This animation illustrates the different types of projectile motion – from free fall to horizontal, vertical, and oblique throws. A projectile moves along its trajectory while the velocity vector is decomposed into its horizontal and vertical components in real time. The launch angle, initial velocity, and time can be adjusted interactively.
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Description of the Animation
The animation shows a projectile moving under the influence of gravitational acceleration \( g = 9.81 \, \text{m/s}^2 \). The object is launched from a starting point with an adjustable initial velocity \( v_0 \) and launch angle \( \theta \). The resulting trajectory – a parabola – is displayed within a coordinate system.
The motion follows the standard equations of projectile motion:
\[ x(t) = v_0 \cos \theta \cdot t \]
\[ y(t) = v_0 \sin \theta \cdot t – \frac{1}{2} g t^2 \]
During the motion, the velocity vector \( \vec{v} \) is displayed at the position of the projectile and decomposed into its components: the horizontal component \( v_x = v_0 \cos \theta \) remains constant, while the vertical component \( v_y = v_0 \sin \theta – g t \) decreases continuously due to gravitational acceleration. A vector parallelogram illustrates the decomposition graphically.
Interactive Controls
The animation offers a variety of interactive options:
- Mode Selection: Four preconfigured scenarios are available – Free Fall (\( \theta = 0° \), \( v_y \) only), Horizontal Throw (\( \theta = 0° \)), Oblique Throw (freely adjustable), and Vertical Throw (\( \theta = 90° \)).
- Launch Angle \( \theta \): Adjustable from 0° to 90°.
- Initial Velocity \( v_0 \): Adjustable from 1 to 40 m/s.
- Time \( t \): Controllable via a slider or via the Play/Pause controls. The time progression can be paused at any point and manually scrubbed forward or backward.
- Play/Pause and Reset: Start and stop the animation or reset it to the initial state.
At the position of the projectile, the total velocity vector \( v \) (black), the horizontal component \( v_x \) (blue), and the vertical component \( v_y \) (red) are shown as arrows. The angle \( \theta \) between the velocity vector and the horizontal is indicated by an arc. Dashed guide lines mark the maximum height and the range of the throw.
Physics Background
Projectile motion is a superposition of two independent motions: uniform motion in the horizontal direction and uniformly accelerated motion in the vertical direction under the influence of gravity. The special cases – free fall, vertical throw, and horizontal throw – arise as limiting cases of general oblique projectile motion for specific launch angles or initial velocities.
The range \( R \) of a projectile launched from ground level is given by:
\[ R = \frac{v_0^2 \sin(2\theta)}{g} \]
The maximum range is achieved at a launch angle of \( \theta = 45° \).
Overview
| Title | Projectile Motion – Trajectory with Velocity Vector Decomposition |
| Target Audience | Teachers and Lecturers |
| License | Open Source – CC BY 4.0 |
| Note on Authorship | Created with AI assistance |