Projectile motion simulator
Set launch speed, angle and height to get range, peak height and flight time from exact kinematics — then scrub along the arc.
Result
v₀ = 20 m/s · θ = 45° · h₀ = 0 m · g = 9.81
45° is the range-maximizing angle from flat ground — any complementary pair (30°/60°) lands at the same spot, just on different clocks.
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position (20.39, 10.19) m · v = (14.14, 0) m/s · speed 14.14 m/s
How is this calculated?
Using the tool
Set the launch speed, angle, and height, and read the whole flight from exact kinematics: how far it lands, how high it climbs, and how long it stays up. Scrub the time slider to fly along the arc — the marker and its velocity vector show where the projectile is and where it's headed at every instant.
The physics
A projectile runs two motions at once, and they don't talk to each other: horizontally it coasts at a constant vₓ = v₀·cos θ, while vertically gravity decelerates, stops, and reverses vy = v₀·sin θ − g·t. That independence is the whole theory: the flight time comes from the vertical equation alone (a quadratic in t — with a launch height, its positive root), the range is just vₓ times that time, and the arc is a parabola because height depends on t². From flat ground the best angle is 45°, where the speed splits evenly between going up and going forward; on the Moon the same throw flies about six times farther only because g divides every vertical term.
New to the math? Learn the concept: Physics of motion, made visual