Back to Hub Projectile Motion
Status Ready
Parameters
Launch Angle (θ) 45°
Initial Velocity (v₀) 30 m/s
Initial Height (h₀) 0 m
Gravity
Options
Trajectory Trail
Velocity Vectors
Slow Motion (0.25×)
📐 Equations & Results
Time t 0.00s
Range x = v₀cosθ · t 0.00m
Height y = h₀+v₀sinθ·t−½gt² 0.00m
Vₓ v₀cosθ 0.00m/s
Vᵧ v₀sinθ − gt 0.00m/s
Speed √(vₓ²+vᵧ²) 0.00m/s
Max Height H —m
Time of Flight T —s
Total Range R —m
Kinetic Energy ½mv² 0.00J
Potential Energy mgh 0.00J
Total Energy KE+PE 0.00J
Impact Angle α —°
Trajectory Curve y(x) = tanθ·x − g/(2v₀²cos²θ)·x² + h₀ —
📖 Governing Equations
x(t) = v₀cosθ · t
y(t) = h₀ + v₀sinθ·t − ½gt²
y(x) = tanθ·x − g/(2v₀²cos²θ)·x² + h₀
Vₓ = v₀cosθ  |  Vỳ = v₀sinθ − gt
|V| = √(Vₓ² + Vỳ²)
Hmax = h₀ + (v₀sinθ)² / (2g)
T = (v₀sinθ + √(v₀sinθ)²+2gh₀)) / g
R = v₀cosθ · T
KE = ½mv²  |  PE = mgh
α = arctan(|Vỳ| / Vₓ) at impact