Ball A solid, ball B (dropped) dashed. Compare x–t (straight line: constant vx)
with y–t (curve: vy grows at −g). Move over the graph to read values.
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Field
h / m
u / m s⁻¹
Mark
R / m
Options
How to use this simulation
Choose the heighth of the bench (or cliff) and the launch speedu — the horizontal speed of the ball
as it leaves the edge.
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 ▶ Launch. Ball A rolls off the edge; ball B is dropped from the edge at the same moment.
The strobe shows the ball every 0.1 s (less often for very long flights). The shadows project each image onto the floor (horizontal motion) and onto
the wall scale (vertical motion): equal steps along the floor, growing steps down the wall.
The landing mark shows the range R. "Carbon paper" adds a ±1 cm scatter, like a real mark.
Press ● Record. The Data tab plots R against u for the current height; gradient = time of flight.
◂ 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
Treat the two directions separately; they share only the time t.
Horizontal: no force, so ax = 0, vx = u (constant),
x = ut.
Vertical: only the weight, so ay = −g, starting from vy = 0:
vy = −gt, h = ½gt².
Time of flight t = √(2h/g) — it depends on the height only, not on u.
Range R = ut. Landing speed v = √(u² + vy²) at
θ = tan⁻¹(|vy|/u) below the horizontal.
Model: no air resistance (see the Air resistance simulation); g = 9.81 (Earth), 1.62 (Moon), 3.71 (Mars) m s⁻². The ball is drawn
bigger than to scale; x and y use the same scale, so the shape of the path is true.