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How It Works
Projectile motion splits into two independent parts: horizontal (constant velocity, x = v₀cosθ·t) and vertical (constant acceleration due to gravity, y = v₀sinθ·t − ½gt²). Together they trace a parabolic trajectory. This calculator solves for distance, velocity, angle, or time in either direction.
Example Problem
A ball is launched at 20 m/s at 45°. How far does it travel horizontally in 2 seconds?
- vₓ = 20 × cos(45°) = 14.14 m/s
- x = 14.14 × 2 = 28.28 m
Frequently Asked Questions
What launch angle gives the maximum range?
On flat ground with no air resistance, 45° maximizes range. With air resistance or from an elevated launch point, the optimal angle is typically less than 45°.
Does air resistance affect projectile motion?
Yes, significantly. Air resistance reduces range and maximum height, and the trajectory is no longer a perfect parabola. These equations assume a vacuum (no air resistance).
Why does horizontal velocity stay constant?
Gravity acts only vertically. With no horizontal force (ignoring air resistance), Newton's first law says the horizontal component of velocity does not change.
Related Calculators
- Constant Acceleration Calculator — solve the underlying 1-D kinematics equations.
- Gravity Equations Calculator — explore gravitational acceleration in detail.
- Force Equation Calculator — find the force behind the acceleration.
- Kinetic Energy Calculator — find the energy of the projectile at any point.
- Potential Energy Calculator — calculate PE at the projectile's maximum height.
- Speed Unit Converter — convert initial velocity between m/s, ft/s, and mph.
Reference: Lindeburg, Michael R. 1992. Engineer In Training Reference Manual. Professional Publication, Inc. 8th Edition.