The current launch is solid; kept launches are faint. vx stays constant, vy falls by
9.81 m s⁻¹ every second and is zero at the top. Move over the graph to read values.
#
Field
u / m s⁻¹
θ / °
h / m
H / m
T / s
R / m
Options
How to use this simulation
Set the launch speedu, the angleθ above the horizontal and the launch heighth
(0 = from the ground).
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. The strobe shows the ball every 0.1 s (less often for very long flights); the dashed lines mark the maximum height H and the range R.
With Keep paths on, earlier launches stay on the screen (faint) so you can compare angles. ↺ Clear removes them.
Press ● Record. The Data tab plots R against θ for the current speed and height, with the theory curve if you want it.
◂ 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
Resolve the launch velocity: ux = u cos θ, uy = u sin θ.
Horizontal: ax = 0, so x = uxt. Vertical:
ay = −g, so y = h + uyt − ½gt², vy = uy − gt.
At the top vy = 0: ttop = uy/g,
H = h + uy²/(2g). The ball still moves sideways at ux.
From the ground (h = 0): T = 2uy/g and R = uxT = u² sin 2θ / g
— largest at 45°, and equal for complementary angles (e.g. 30° and 60°).
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.