Solid = with air resistance, dashed = vacuum (same launch). With air, vx is no longer constant and
vy–t is no longer a straight line.
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Object
u / m s⁻¹
θ / °
R air / m
R vacuum / m
H air / m
Show
How to use this simulation
Choose an object, the launch speed and angle. Press ▶ Launch.
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.
The solid path is the real one, with air resistance; the dashed path is the same launch in a vacuum.
The free-body diagram shows the weight W, the drag Fd (always opposite to the velocity) and their resultant.
Press ● Record. The Data tab plots the range against the angle, with and without air.
◂ 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
Drag: Fd = ½ρCdAv², opposite to the velocity. It grows quickly with speed.
Light, large objects (ping-pong ball, shuttlecock) are affected most: their drag soon becomes comparable to their weight.
Effects: shorter range, lower top, steeper fall than rise, time down longer than time up, best angle below 45°.
Falling fast enough, drag balances the weight: mg = ½ρCdAvt² (terminal speed).
Model: ρ = 1.20 kg m⁻³, Cd constant for each object, no wind and no spin. At SL, air resistance is treated
qualitatively; the numbers here help you see the effects.