➡️ Horizontal Projectile Motion Calculator
Calculate horizontal projectile motion
How to Use This Calculator
Enter Initial Velocity
Input the initial horizontal velocity (v₀) in m/s. This is the speed at which the object is launched horizontally (parallel to the ground). Convert from km/h by dividing by 3.6.
Enter Launch Height
Enter the height (h) in meters from which the object is launched horizontally. This is the vertical distance above the ground at the launch point.
Enter Gravity (Optional)
The default is 9.81 m/s² (Earth's gravity). You can change this for other planets or precision. Moon = 1.62 m/s², Mars = 3.71 m/s².
Click Calculate
Press "Calculate" to find the time of flight, horizontal range, and final velocity at impact.
Formula
t = √(2h/g)
R = v₀ × t
v = √(v₀² + v_y²) where v_y = gt
Where:
- v₀ = Initial horizontal velocity (m/s)
- h = Launch height (m)
- g = Acceleration due to gravity (9.81 m/s²)
- t = Time of flight (s)
- R = Horizontal range (m)
- v = Final velocity magnitude (m/s)
- v_y = Final vertical velocity component (m/s)
Example Calculation:
A ball thrown horizontally at 10 m/s from 20 m height:
1. Time of flight: t = √(2 × 20 / 9.81) = √(4.08) = 2.02 s
2. Range: R = 10 × 2.02 = 20.2 m
3. Final velocity: v_y = 9.81 × 2.02 = 19.8 m/s, v = √(10² + 19.8²) = 22.2 m/s
About Horizontal Projectile Motion Calculator
The Horizontal Projectile Motion Calculator determines the trajectory, range, and velocity of an object launched horizontally from a height. This is a special case of projectile motion where the initial vertical velocity is zero, simplifying the calculations while demonstrating key physics principles.
Key Principles
- Independent Motion: Horizontal and vertical motions are independent. Horizontal velocity remains constant (no acceleration), while vertical motion accelerates due to gravity.
- Time of Flight: Determined solely by vertical motion (fall height). Higher launch points result in longer flight times, regardless of horizontal speed.
- Range: The product of constant horizontal velocity and time of flight. Faster horizontal speed or greater height increases range.
- Trajectory: The path forms a parabola. The object follows a curved path downward while maintaining constant horizontal speed.
Horizontal vs. Angled Launch
Horizontal launch (this calculator) simplifies projectile motion because there's no initial vertical velocity component. For angled launches, use the general projectile motion calculator. Horizontal launches are common in scenarios like objects rolling off tables, water from fountains, or packages dropped from aircraft.
Practical Applications
- Physics Education: Understand the independence of horizontal and vertical motion, a fundamental concept in mechanics.
- Sports: Analyze trajectories of horizontally thrown objects, water jets, or objects rolling off surfaces.
- Engineering: Design delivery systems, calculate drop zones for airdrops, or analyze flow from horizontal nozzles.
- Safety Planning: Determine safe distances for objects falling from heights, important in construction and workplace safety.
Understanding the Results
Time of Flight: How long the object takes to fall to the ground. This depends only on height, not horizontal speed. Double the height = √2 × the time (about 1.41× longer).
Range: Horizontal distance traveled. Since horizontal velocity is constant, range = speed × time. Faster horizontal speed or longer flight time increases range.
Final Velocity: The speed at impact combines constant horizontal velocity with the accumulated vertical velocity from falling. The impact angle depends on the ratio of these components.
Frequently Asked Questions
Why does horizontal velocity stay constant?
There's no horizontal acceleration (assuming no air resistance). Gravity acts only downward, so horizontal motion is unaffected. This demonstrates the independence of horizontal and vertical motion - a key principle in projectile motion.
Does horizontal speed affect fall time?
No! Time of flight depends only on height. Whether thrown at 1 m/s or 100 m/s horizontally, if dropped from the same height, the fall time is identical. Horizontal speed only affects how far it travels horizontally (range).
What if there's air resistance?
This calculator assumes no air resistance. Real-world objects experience drag that reduces horizontal velocity and slightly affects fall time. For dense objects or short distances, the approximation is good. For light objects or long falls, air resistance becomes significant.
How do I find the impact angle?
Impact angle = arctan(v_y / v₀) where v_y = gt (final vertical velocity) and v₀ is horizontal velocity. Faster horizontal speed or shorter fall time results in a shallower impact angle.
Can I use this for objects launched at an angle?
This calculator is specifically for horizontal launches (0° launch angle). For angled launches, use the general projectile motion calculator, which accounts for both horizontal and vertical initial velocity components.
What happens if I double the horizontal speed?
Doubling horizontal speed doubles the range, since range = v₀ × t and time of flight is unchanged. The object travels twice as far horizontally but takes the same time to fall.