Height of a Projectile Calculator in Feet
Calculate and visualize the height of a projectile at any point in its trajectory based on physics equations.
Input Parameters
Range: 0 to 1000 ft/s
Range: 0 to 90 degrees
Range: 0 to 1000 feet
Enter time to calculate height at a specific moment
Calculation Methods
Calculate the projectile’s height at a specific time during its flight.
Formula:
h = h₀ + v₀sin(θ) × t – (1/2)gt²
Where:
h = Height at time t
h₀ = Initial height
v₀ = Initial velocity
θ = Launch angle
t = Time
g = 32.2 ft/s² (gravity)
Calculate the maximum height the projectile will reach during its flight.
Formula:
h_max = h₀ + (v₀sin(θ))²/(2g)
Where:
h_max = Maximum height
h₀ = Initial height
v₀ = Initial velocity
θ = Launch angle
g = 32.2 ft/s² (gravity)
Results
Height at Time
0.00 ft
At t = 0s
Maximum Height
0.00 ft
Reached at t = 0s
Time of Flight
0.00 s
Total time in air
Range
0.00 ft
Horizontal distance traveled
Trajectory Visualization
Understanding Projectile Motion
What is Projectile Motion?
Projectile motion is the motion of an object thrown or projected into the air, subject only to the acceleration of gravity. The path followed by a projectile is called its trajectory.
Projectile motion is a form of two-dimensional motion, consisting of:
- Horizontal motion at constant velocity (ignoring air resistance)
- Vertical motion with constant acceleration due to gravity
Key Equations
Horizontal Position
x = x₀ + v₀cos(θ) × t
The horizontal position changes at a constant rate.
Vertical Position (Height)
h = h₀ + v₀sin(θ) × t – (1/2)gt²
The vertical motion is affected by gravity.
Time to Maximum Height
t_max = v₀sin(θ)/g
Time taken to reach the highest point.
Maximum Height
h_max = h₀ + (v₀sin(θ))²/(2g)
The highest point the projectile reaches.
Practical Applications
Sports
Basketball shots, football passes, golf swings, and baseball throws all involve projectile motion.
Engineering
Used in designing water fountains, catapults, and in calculating safety distances for demolition work.
Military
Calculation of artillery trajectories and missile paths.
Tips for Using This Calculator
- For most accurate results, enter values that match realistic scenarios.
- To maximize distance, a launch angle of 45° is typically optimal (without air resistance).
- Higher initial velocities result in greater heights and distances.
- Note that this calculator doesn’t account for air resistance, which would reduce both height and distance in real-world applications.
- The animation provides a visual understanding of how changing parameters affects the trajectory.
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