STUCK IN PHYSICSOne launch. Every instant.
Launch above, along or below the horizontal. Scrub through the flight to see how the velocity changes while gravity stays the same.
Build your launch
Air resistance
Fdrag = cv², opposite the velocity. The slider sets resistance strength; the force itself changes during flight.
Right is +x. Up is +y. Gravity is constant. Air is at rest; set drag to zero for ideal projectile motion.
Changing launch settings returns time to zero.
The flight
Velocity arrows use one fixed velocity scale for this launch. Acceleration uses a separate scale. The flight axes use equal horizontal and vertical distance scales. Acceleration shows the resultant of gravity and air resistance.
The flight, as time graphs
Time marker: 0.00 s
The dashed time marker follows the animation. Tap a graph to jump to that instant, or focus a graph and use the left/right arrow keys. Each graph keeps a fixed scale throughout the current flight.
Δx and Δy are measured from the launch point: Δy = y − h. Displacement magnitude is the straight-line distance from the launch point, not distance travelled. Speed is the magnitude of velocity. Acceleration includes drag when enabled; plots stop just before impact.
The model
Ideal-motion equations below apply only when drag = 0. With drag enabled, the trajectory is computed numerically from Newton’s second law.
y = h + (u sin θ)t − ½gt²
vₓ = u cos θ · vᵧ = u sin θ − gt
Time of flight is the first ground contact after launch. For an upward launch from ground level, it is the later positive root of y = 0. A downward or horizontal launch starting on the ground has zero airborne time.
The simulation ends at contact. Velocity shown at the endpoint is just before impact; a bounce or collision is not modelled.
Predict, then check
At the highest point, is velocity zero—or only its vertical component?
For a horizontal launch with drag set to zero, does changing the speed change the time to hit the ground? Now enable drag and compare.
Launch below the horizontal. Gravity stays constant, but how does drag change the resultant acceleration?
At exactly ±90°, motion is vertical. With no drag and non-zero horizontal speed, the trajectory is parabolic. Air resistance makes the trajectory non-parabolic. At zero speed the object is dropped.