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Projectile Motion Calculator

Calculate max height, range, and flight time for a projectile launched at an angle.

Projectile motion describes the path of an object launched into the air at an angle, influenced only by gravity. It is a classic problem in physics combining horizontal (constant velocity) and vertical (accelerated) motion.

The key equations are: Maximum Height = (v₀ sin θ)² / (2g), Range = v₀² sin(2θ) / g, and Time of Flight = 2v₀ sin θ / g. These assume flat terrain, no air resistance, and launch from ground level.

The maximum range occurs at 45 degrees. Complementary angles (like 30° and 60°) produce the same range but different trajectories. A ball thrown at 30 m/s at 45° travels about 91.8 meters. Air resistance in reality reduces range significantly, especially for light or high-drag objects.

Frequently Asked Questions

At what angle is range maximized?
45 degrees gives the maximum range in a vacuum. With air resistance, the optimal angle is slightly lower (around 40–43 degrees).
Does mass affect projectile range?
In a vacuum, no. All masses follow the same trajectory. In air, heavier objects travel farther because air resistance has less relative effect.
Why is this called 'ideal' projectile motion?
It ignores air resistance, wind, spin, and altitude variations. Real projectiles (balls, bullets, rockets) behave differently due to these factors.
Projectile Motion Calculator
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