Horizontal Projectile Motion Calculator

How it works

1. 1Enter the horizontal launch speed (v₀) and the height above the ground from which the object is launched.
2. 2The calculator uses t = √(2h ÷ g) to find the time of flight, then multiplies by v₀ to get the horizontal range.
3. 3Impact speed is computed as √(v₀² + (g·t)²), combining the unchanged horizontal velocity with the vertical velocity gained while falling.

Use cases

• Estimating where a ball rolling off a table will land on the floor.
• Calculating the range of a horizontally fired projectile from a cliff or elevated platform.
• Physics coursework involving two-dimensional kinematics with no initial vertical velocity.

Frequently asked questions

What formula is used for time of flight?

For a horizontal launch the initial vertical velocity is zero, so the object falls freely: t = √(2h ÷ g), where h is the launch height and g ≈ 9.81 m/s². For example, launching from h = 20 m gives t = √(2 × 20 ÷ 9.81) ≈ 2.02 s.

How is the horizontal range calculated?

Because there is no horizontal acceleration (air resistance ignored), range = v₀ × t. With v₀ = 10 m/s and t ≈ 2.02 s, range ≈ 10 × 2.02 = 20.2 m.

Does this calculator account for air resistance?

No. It assumes ideal conditions with no air resistance and a uniform gravitational field (g = 9.81 m/s²). Real-world ranges are shorter for objects with significant drag, such as lightweight balls or fast-moving objects.