Projectile Motion Calculator (Range, Height, Time)
Range, maximum height and time of flight for a projectile launched from level ground.
Result
Range (R)
63.7105 m
Max Height (H)
15.9276 m
Time of Flight (T)
3.604 s
u_x (horizontal)
17.6777 m/s
u_y (vertical)
17.6777 m/s
Concept
Projectile motion is the motion of a body thrown at an angle to the horizontal under gravity alone, with no air resistance. Horizontal and vertical components are independent — the hallmark of the principle of superposition.
The horizontal velocity stays constant (no acceleration), while the vertical component changes at g = 9.8 m/s². This gives the characteristic parabolic trajectory.
Maximum range is achieved at θ = 45°. Complementary angles (e.g. 30° and 60°) give the same range but different heights and times of flight.
Formula
Range (R)=u2 sin 2θg
Max Height (H)=u2 sin2θ2g
Time of flight (T)=2u sinθg
Variables
um/s- Initial speed of projection.
θ°- Angle of projection above horizontal.
gm/s²- Acceleration due to gravity — 9.8 m/s² on Earth.
Rm- Horizontal range.
Hm- Maximum height above launch point.
Ts- Total time of flight.