This animation illustrates the different types of projectile motion – from free fall to horizontal, vertical, and oblique throws. A projectile moves along its trajectory. The velocity vector is decomposed into its 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 following parameters are adjustable:
- Mode Selection: Four preconfigured scenarios are available – Free Fall (\( v_0 = 0 \), \( v_y \) from gravity 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.
Physical Background
Projectile motion superimposes two independent motions: uniform horizontal motion and uniformly accelerated vertical motion under 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 |
| Features | Full-screen mode Lossless scaling Large screens and projectors supported |
| License | Open Source – CC BY 4.0 |
| Note on Authorship | Created with AI assistance |