Projectile Motion
Study how objects travel through the air under gravity. Horizontal velocity stays constant while vertical velocity changes, producing a curved parabolic path.
Learning Path
Projectile Motion Poster
Visual overview of trajectory equations, launch angles, and key formulas including range, max height, and time of flight.
Open →Projectile Motion Calculator
Enter initial velocity, launch angle, and height. Drag the time slider to step through the flight path and see position and velocity at any moment.
Open →Gravity and Orbits Lab
Set central mass, semi-major axis, and eccentricity to animate elliptical orbits and explore how gravity governs all projectile and orbital motion.
Open →Key Formulas
The core kinematic formulas for projectile motion.
- Range: R = v0^2 sin(2theta) / g
- Max height: H = (v0 sin(theta))^2 / 2g
- Time of flight: T = 2v0 sin(theta) / g
- Horizontal: x = v0 cos(theta) * t
- Vertical: y = v0 sin(theta) * t - (1/2)gt^2
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Common Questions
What makes projectile motion parabolic?
Horizontal velocity is constant (no air resistance) while vertical velocity changes due to gravity at a constant 9.8 m/s^2 downward. Combining constant horizontal motion with accelerating vertical motion produces a parabolic path.
Which launch angle gives the maximum range?
A 45-degree angle gives maximum range on level ground. Complementary angles such as 30 and 60 degrees produce the same range but different maximum heights and flight times.