Horizontal Projectile Motion Calculator
Calculate time of flight, range, and trajectory for objects launched horizontally
Calculate Horizontal Projectile Motion
Horizontal launch velocity (no vertical component)
Height above ground level
Earth: 9.81 m/s², Moon: 1.62 m/s², Mars: 3.71 m/s²
Projectile Motion Results
Key Formulas:
• Time of Flight: t = √(2h/g)
• Range: x = v × t
• Trajectory: y = h - (g×x²)/(2×v²)
Physics Analysis
Example: Ball from Eiffel Tower
Problem Setup
Scenario: A ball is thrown horizontally from the Eiffel Tower's observation deck
Initial velocity: 7 m/s (horizontal)
Height: 276 m (observation deck)
Gravity: 9.81 m/s² (Earth)
Step-by-Step Solution
1. Time of flight: t = √(2h/g) = √(2×276/9.81) = √56.27 = 7.50 s
2. Horizontal range: x = v×t = 7×7.50 = 52.5 m
3. Final vertical velocity: vy = g×t = 9.81×7.50 = 73.6 m/s
4. Final velocity: v = √(vx² + vy²) = √(7² + 73.6²) = 73.9 m/s
5. Impact angle: θ = arctan(73.6/7) = 84.6° below horizontal
Quick Scenarios
Basketball Shot
Ball from Balcony
Eiffel Tower Drop
Airplane Drop
Physics Principles
Horizontal Motion
Constant velocity (no acceleration)
Vertical Motion
Free fall with gravitational acceleration
Independence
Horizontal and vertical motions are independent
Parabolic Path
Trajectory follows parabolic curve
Key Equations
Time of Flight
t = √(2h/g)
Horizontal Range
x = v × t
Trajectory Equation
y = h - (gx²)/(2v²)
Final Velocity
v = √(vx² + vy²)
Understanding Horizontal Projectile Motion
What is Horizontal Projectile Motion?
Horizontal projectile motion occurs when an object is launched horizontally from an elevated position with zero initial vertical velocity. The object follows a parabolic path under the influence of gravity alone.
Key Characteristics
- •Initial vertical velocity is zero
- •Horizontal velocity remains constant
- •Vertical motion is free fall
- •Launch angle is 0° (horizontal)
Motion Analysis
Horizontal Component
- • Velocity: vx = v (constant)
- • Acceleration: ax = 0
- • Position: x = v × t
Vertical Component
- • Initial velocity: vy₀ = 0
- • Acceleration: ay = g (downward)
- • Position: y = h - ½gt²
- • Velocity: vy = gt
Real-World Applications
Sports
Basketball shots, soccer kicks, golf drives
Engineering
Water fountain design, projectile weapons
Aviation
Cargo drops, bomb trajectories
Entertainment
Stunt jumps, fireworks displays
Assumptions & Limitations
Assumptions
- • No air resistance
- • Uniform gravitational field
- • Flat Earth approximation
- • Point mass object
Real-World Factors
- • Air resistance affects trajectory
- • Wind can alter path
- • Object shape and size matter
- • Spin can cause curve