keisoku

Projectile Motion Calculator from Flight Time and Range

Enter the flight time and horizontal range to back-calculate the launch speed, launch angle, and peak height for ideal projectile motion without air resistance.

Input

Enter the flight time and horizontal range to back-calculate the launch speed, launch angle, and peak height of the projectile.

s

Time from launch to landing, in seconds.

m

Horizontal distance from launch point to landing point, in meters.

The standard gravity g = 9.80665 m/s² is used.

Result

Launch speed v0

19.853492m/s

Launch angle θ = 47.810385 degrees

Maximum height

11.032481 m

Launch speed (km/h)

71.472571 km/h

Horizontal component

13.333333 m/s

Vertical component

14.709975 m/s

θ = 47.810385 degPeak 11.032481 mRange 40 m

Using vx = R / T and vy = g T / 2, the launch speed and angle are derived, and the maximum height is vy² / (2g). Air resistance is ignored.

How it works

  • The launch point and landing point are assumed to be at the same height (level ground), and air resistance is ignored.
  • The horizontal velocity component is vx = R / T and the vertical launch component is vy = g T / 2.
  • The launch speed is v0 = sqrt(vx² + vy²) and the launch angle is atan2(vy, vx) converted to degrees.
  • The maximum height is Hmax = vy² / (2g) = g T² / 8.
  • The standard gravity g = 9.80665 m/s² is used.

Reviews

Tell us what you think of this calculator.

Write a review

  1. Home

  2. Projectile Motion Calculator from Flight Time and Range