Time of Flight Calculator
Calculate how long a projectile stays in the air during projectile motion
Calculate Time of Flight
Speed at which projectile is launched
Angle above horizontal (0° = horizontal, 90° = vertical)
Height above ground level (0 = ground level)
m/s² (Earth: 9.81, Moon: 1.62, Mars: 3.71)
Time of Flight Results
Formula used: t = 2 × V₀ × sin(α) / g
Input values: V₀ = 0.00 m/s, α = 45.0°, h = 0.00 m
Physics: Ground level launch - air resistance neglected
Physics Analysis
Example Calculations
Grand Canyon Pebble Drop
Initial velocity: 16 ft/s (4.88 m/s)
Launch angle: 20°
Initial height: 6,000 ft (1,829 m)
Gravity: 9.81 m/s²
Calculation
t = [V₀ × sin(α) + √((V₀ × sin(α))² + 2 × g × h)] / g
V₀ × sin(20°) = 4.88 × 0.342 = 1.67 m/s
t = [1.67 + √(1.67² + 2 × 9.81 × 1829)] / 9.81
t = [1.67 + √(2.79 + 35,901)] / 9.81
t ≈ 19.5 seconds
Basketball Shot
Initial velocity: 7 m/s
Launch angle: 45°
Initial height: 2 m (player's release point)
Time of flight: ≈ 1.2 seconds
Projectile Motion Phases
Launch
Initial velocity at angle α
V₀ₓ = V₀ cos(α), V₀ᵧ = V₀ sin(α)
Ascent
Rising to maximum height
Vᵧ decreases due to gravity
Peak
Maximum height reached
Vᵧ = 0, only Vₓ remains
Descent
Falling to ground level
Vᵧ increases downward
Impact
Projectile hits ground
End of flight time
Launch Angle Effects
Tip: 90° gives maximum flight time for a given velocity
Physics Tips
Time of flight depends on vertical motion only
Horizontal velocity remains constant (no air resistance)
Higher launch angles increase flight time
Initial height extends total flight time
Gravity affects vertical motion throughout flight
Understanding Time of Flight in Projectile Motion
What is Time of Flight?
Time of flight is the total duration a projectile remains in the air from launch until it returns to ground level (or hits an obstacle). It's determined primarily by the vertical component of motion and the initial height.
Key Physics Principles
- •Independent motion: horizontal and vertical motions are independent
- •Gravity affects only vertical motion
- •No air resistance assumed
- •Parabolic trajectory path
Time of Flight Formulas
Ground Level Launch (h = 0)
t = 2 × V₀ × sin(α) / g
Elevated Launch (h > 0)
t = [V₀ × sin(α) + √((V₀ × sin(α))² + 2gh)] / g
Variable Definitions
- t: Time of flight (s)
- V₀: Initial velocity (m/s)
- α: Launch angle (radians)
- g: Gravitational acceleration (m/s²)
- h: Initial height (m)
Factors Affecting Time of Flight
Increases Flight Time
- • Higher launch angle (up to 90°)
- • Greater initial velocity
- • Higher initial height
- • Lower gravitational acceleration
Decreases Flight Time
- • Lower launch angle (toward 0°)
- • Lower initial velocity
- • Ground level launch
- • Higher gravitational acceleration
Real-World Applications
Sports
Basketball shots, soccer kicks, golf drives
Military
Artillery, ballistics, missile trajectories
Engineering
Water fountains, vehicle jumps, safety systems