Projectile Motion Calculator (Velocity, Angle, Time)

From initial speed, launch angle, and elapsed time, find the position (x, y) and velocity at that instant, with a trajectory sketch.

Input

Enter the initial speed, launch angle, and elapsed time to compute the position and velocity at that instant. Air resistance is ignored.

Initial speed v0

m/s

Speed at the moment of launch, in meters per second

Launch angle θ

deg

Angle above the horizontal, in degrees

Elapsed time t

Time elapsed since launch, in seconds

Uses standard gravity g = 9.80665 m/s² for the acceleration.

Position (x, y) at 1.5 s

(21.213203, 10.180722)

Values in meters, measured from the launch point

Speed

14.153531 m/s

Height y

10.180722 m

Horizontal velocity vx

14.142136 m/s

Vertical velocity vy

-0.567839 m/s

Velocity direction

-2.299323 deg

Peak height

10.197162 m

x = v0 cosθ · t, y = v0 sinθ · t − (1/2) g t², vx = v0 cosθ, vy = v0 sinθ − g t. Air resistance is not considered.

The launch point is the origin (0, 0) and air resistance is ignored, modeling ideal projectile motion. Gravity uses standard gravity g = 9.80665 m/s² directed downward.
At the entered elapsed time t, the position is x = v0 cosθ · t horizontally and y = v0 sinθ · t − (1/2) g t² vertically, where θ is the launch angle.
Velocity components are horizontal velocity vx = v0 cosθ (constant) and vertical velocity vy = v0 sinθ − g t. Speed is the square root of the sum of their squares, and the direction is given as an angle from the horizontal.
The reference peak height is ymax = (v0 sinθ)² / (2g) and the time to apex is v0 sinθ / g. When the launch angle is horizontal or below, no rise occurs, so the peak height equals the launch height (0).
A negative y means the object is below the launch point at that instant. Air resistance, terrain, and spin are not considered.

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