Projectile Motion
Solve time of flight T = 2v sinθ/g, range R = v² sin(2θ)/g, and max height H = v² sin²θ/(2g). Free calculator with step-by-step formulas.
Key formula
Range, time, and height formulas for 2D motion
How do you calculate time of flight in projectile motion?
On level ground, time of flight is T = 2 v sinθ / g (or T = 2 vy / g with vy = v sinθ). Then range R = v² sin(2θ) / g and max height H = v² sin²θ / (2g). Enter v and θ in degrees; the calculator converts internally.
About this tool
Projectile motion splits a launch into constant horizontal velocity and vertical motion under gravity. This page keeps the intro-physics formulas for time of flight (tiempo de vuelo), range, and maximum height visible so you can check homework launched from level ground with no air resistance.
How to use this calculator
- Choose the variable you want to solve for and confirm which values are already known.
- Enter inputs in consistent units before calculating so the formula is applied correctly.
- Check whether the result is physically reasonable by comparing it with the size of the inputs.
- Use the step-by-step breakdown to see how the equation was rearranged and evaluated.
Worked examples
Example 1: time of flight at 20 m/s, 45°
v = 20 m/s, θ = 45°, g = 9.8. T = 2(20)sin45° / 9.8 ≈ 2.886 s (peak at T/2 ≈ 1.443 s). R = 400 / 9.8 ≈ 40.82 m. H ≈ 10.20 m.
Example 2: solve for time at 30 m/s, 30°
v = 30 m/s, θ = 30°, g = 9.8. vy = 15 m/s. T = 2(15) / 9.8 ≈ 3.061 s. R ≈ 79.55 m. H ≈ 11.48 m. Same speed at 60° keeps R but raises T and H.
Example 3: straight up at 10 m/s
θ = 90°, v = 10 m/s, g = 9.8. T = 2(10)/9.8 ≈ 2.041 s. R = 0. H ≈ 5.10 m — same as 1D free-fall up and down.
Frequently asked questions
What is the time of flight formula?
For level ground with no air resistance, T = 2 v sinθ / g. It is twice the time to reach maximum height (vy / g).
How do you solve for time in projectile motion?
Find vy = v sinθ, then T = 2 vy / g when landing height equals launch height. If Δy ≠ 0, solve the quadratic Δy = vy t − ½ g t² instead — this calculator is the same-level case.
What is the projectile range formula?
On level ground, R = v² sin(2θ) / g. Maximum range is at θ = 45° for a given speed.
What is the maximum height formula?
H = v² sin²θ / (2g). Only the vertical component vy = v sinθ stores the height.
Does this include air resistance?
No. This is the ideal classroom model: constant g, no drag, flat landing. Real balls and bullets fall short of these ranges.