Ball A solid, ball B dashed. Move the mouse (or your finger) over the graph to read values. Up is positive, so a falling ball has a
negative velocity. The gradient of y–t is v; the gradient of v–t is a.
#
Object
Field
h / m
v₀ / m s⁻¹
Timing
t / s
t² / s²
Options
How to use this simulation
Choose the release heighth and the launch velocityv₀. With v₀ = 0 the ball is
dropped; positive v₀ throws it up, negative v₀ throws it down.
Set the values with the sliders, or type a value in the box next to a slider and press Enter. A value outside the allowed range is set to the nearest allowed value.
Press ▶ Drop (or ▶ Throw). The strobe shows where the ball was every 0.1 s (less often for very long falls) — the gaps grow
because the ball speeds up. Slow ¼× plays the motion at a quarter of real speed (the times stay real).
Add ball B to drop two objects side by side. Switch air resistance on (Earth only) to see when mass matters.
Timing: the light gate gives the exact time; stopwatch adds a human reaction time (0.15–0.25 s) when
you start and when you stop, like the class experiment.
Press ● Record. The Data tab plots h against t² for the drops; gradient = g/2.
◂ 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
Up is positive. In a vacuum only the weight acts, so every object has a = −g (g = 9.81 m s⁻² on Earth),
whatever its mass.
s = ut + ½at² · v = u + at · v² = u² + 2as · s = ½(u + v)t
Dropped from rest through height h: h = ½gt², so t = √(2h/g) and
v = √(2gh).
Thrown up at u: top after t = u/g, max height above the hand = u²/(2g),
back at the hand after 2u/g.
With air resistance: Fd = ½ρCdAv² opposes the motion; the resultant is
smaller than W, so a light, large object falls more slowly.
Model: g = 9.81 (Earth), 1.62 (Moon), 3.71 (Mars) m s⁻²; air density 1.20 kg m⁻³. The balls are drawn bigger
than to scale. The Moon and Mars have no (or almost no) air, so air resistance is only available on Earth.