Enter your initial velocity and initial height to calculate the full trajectory of a horizontally launched projectile. This Horizontal Projectile Motion Calculator computes time of flight, horizontal range, vertical velocity at impact, and total impact speed — with a chart showing the parabolic path.
Horizontal Range
--
Time of Flight
--
Vertical Velocity at Impact
--
Total Impact Speed
--
Impact Angle (below horizontal)
--
The horizontal distance (range) is calculated using the formula x = V₀ × t, where V₀ is the initial horizontal velocity and t is the time of flight. Since there is no horizontal acceleration, the projectile travels at a constant horizontal speed throughout its flight. First calculate the time of flight from the height, then multiply by the initial velocity.
The time of flight depends only on the initial height and gravity: t = √(2y₀ / g). Because the initial vertical velocity is zero, the projectile falls freely under gravity. A greater height means a longer flight time regardless of the horizontal speed.
No — in ideal projectile motion (ignoring air resistance), there is no horizontal acceleration. The horizontal component of velocity remains constant throughout the entire flight. Only the vertical component changes due to gravitational acceleration.
The vertical acceleration equals the gravitational acceleration, g ≈ 9.81 m/s² downward on Earth. This is the same as free fall — the horizontal velocity has no effect on vertical motion. On other planets, the vertical acceleration equals that planet's surface gravity.
No, this calculator assumes ideal projectile motion with no air resistance. In reality, air drag reduces both the range and time of flight. For most introductory physics problems, the no-air-resistance model is the standard assumption.
In horizontal projectile motion, the object is launched purely horizontally — its initial vertical velocity is zero. In general projectile motion, the object is launched at an angle, giving it both horizontal and vertical initial velocity components. This calculator specifically handles the horizontal launch case.
The trajectory is a parabola. Because horizontal velocity is constant and vertical velocity increases linearly with time due to gravity, the resulting path follows the equation y = y₀ − (g × x²) / (2 × V₀²). This is a downward-opening parabola starting at the launch point.
The impact speed is the magnitude of the velocity vector at the moment of landing. It combines the unchanged horizontal velocity (Vx = V₀) and the vertical velocity at impact (Vy = g × t) using the Pythagorean theorem: V_impact = √(V₀² + Vy²). The impact angle below the horizontal is arctan(Vy / V₀).