Calculator · Engineering Mechanics
Projectile Motion Calculator
Ideal projectile motion of a point particle in a uniform gravitational field, with an explicit landing elevation that need not equal the launch height.
Launch
Magnitude of the field, which acts along −y.
Trajectory
Results
| Launch components (v₀x, v₀y) | (7.0711, 7.0711) m/s |
|---|---|
| Time to apex | 0.7208 s |
| Maximum height | 2.5484 m |
| Apex position | (5.0968, 2.5484) m |
| Flight time to the landing elevation | 1.4416 s |
| Horizontal range | 10.194 m |
| Impact velocity | (7.0711, -7.0711) m/s |
| Impact speed | 10 m/s |
| Impact angle from +x | -45° |
Technical reference
x(t) = x₀ + v₀·cosθ · t
y(t) = y₀ + v₀·sinθ · t − ½·g·t²
t_apex = v₀·sinθ / g (only when v₀·sinθ > 0)
- x₀, y₀
- launch position[m]
- v₀, θ
- launch speed and angle from +x[m/s, deg]
- g
- gravity magnitude, acting along −y[m/s²]
- t
- time since launch[s]
Flight time and range are the roots of ½·g·t² − v₀·sinθ·t + (y_land − y₀) = 0 for the chosen landing elevation; they are only reported when a future intersection exists. The familiar closed forms t = 2v₀sinθ/g and R = v₀²sin(2θ)/g hold only in the special case y_land = y₀ (level launch and landing) — deliberately not shown as a general formula here, since this calculator allows an arbitrary landing elevation.
Assumptions
- · Point particle: no size, no spin and no lift.
- · Uniform gravitational field of the stated magnitude, acting along −y.
- · No aerodynamic drag; this is the ideal trajectory, not a measured flight path.
- · Events are only reported when they occur at a future time; nothing imaginary is shown as a result.
Continue
The same launch position, velocity components and gravity, as a dynamic particle model.