The orange line marks the time probe. The speed is smallest at the top, where only vx is left.
Direction φ is measured from the horizontal (positive = above).
#
t / s
x / m
y / m
vx / m s⁻¹
vy / m s⁻¹
v / m s⁻¹
φ / °
Show
How to use this simulation
Set the launch speed, angle (negative = thrown downward) and height. Press ▶ Launch, or set the
time probe (▼ ▲, or click and drag on the graph) to any moment of the flight.
Set each value with ▼ and ▲ (hold to go faster; the ↑ ↓ keys or the mouse wheel in the box also work, Shift = ×10), or type a value in the box. ↺ puts it back to its start value. Outside the classroom range the box turns amber ⚠: fine to explore, but the lab can't do this.
Move the pointer over any graph (or tap it): a dashed line shows the values where it cuts each curve, or the values of the nearest data point.
Vectors draws the velocity every 0.2 s along the path; Components adds vx (purple) and
vy (blue).
The velocity diagram (middle column) draws all those velocities from one point. Their tips lie on a vertical line,
equally spaced: every 0.2 s the velocity changes by the same amount, Δv = gΔt, straight down.
● Record reading saves the probe values. The Data tab plots vy against t:
gradient = −g, intercept = uy.
◂ 0.1 s / 0.1 s ▸ (or the ← → keys) step the motion back and forward and pause it, so you can discuss
each moment: the velocity and acceleration arrows stay on the screen. Graph tools: Area shades the area under
a velocity graph (= displacement) or an acceleration graph (= change in velocity) up to that moment and writes what the area is (its name and value) inside it; Tangent draws the
tangent there (gradient of a position graph = velocity, of a velocity graph = acceleration).
Work through the Tasks tab. Write explanations on your worksheet.
The physics
vx = u cos θ (constant) · vy = u sin θ − gt
speed v = √(vx² + vy²) · direction φ = tan⁻¹(vy / vx)
At height y: vy² = uy² − 2g(y − h), so the speed depends only on the height —
the same on the way up and on the way down.
Acceleration: a = Δv/Δt = g downward, everywhere on the path.
Model: no air resistance (see the Air resistance simulation); g = 9.81 (Earth), 1.62 (Moon), 3.71 (Mars) m s⁻².
Newton's laws
The badge above the scene says which law applies at this moment: 1st law — at rest or moving at a constant velocity, the resultant force is zero (ΣF = 0); 2nd law — accelerating, ΣF = ma. The table under the free-body diagram adds up the forces (ΣF) and compares them with m a (▾ folds it). Tick 3rd-law pairs to see every force with its partner: the same size and type, in the opposite direction, acting on the other body (the Earth, the floor, the string, the fluid…).