Terminal Velocity
Drop shapes through fluid. Builds on Newton's Three Laws.
A skydiver jumps from a plane. After about 12 seconds of free fall, they stop accelerating and fall at a constant speed.
What's happening physically when they stop accelerating?
At terminal velocity, air resistance exactly equals weight: F_drag = mg. Since net force = 0, acceleration = 0 (Newton's 2nd law). The skydiver still FALLS — they just stop ACCELERATING. For a typical skydiver, this is about 55 m/s (200 km/h) belly-down, or 90 m/s (320 km/h) head-down.
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Drop different shapes through fluid. Watch the force arrows — when drag equals weight, the object stops accelerating.
v_t = √(2mg/ρCₐA)
Heavier objects have higher terminal velocities. A bowling ball and a beach ball have the same shape but vastly different masses — the bowling ball falls MUCH faster in air.
A parachute increases area A by ~100× and drag coefficient by ~3×. This drops terminal velocity from ~200 km/h to ~20 km/h — survivable!
Without air resistance, rain falling from 2 km would hit at 200 m/s — lethal! Terminal velocity limits small raindrops to ~9 m/s. The atmosphere literally saves our lives.
A cat's terminal velocity is about 100 km/h (vs 200 km/h for humans). Their lower mass-to-area ratio means they reach terminal velocity faster and survive falls from remarkable heights.
“Terminal velocity isn't about gravity giving up — it's about drag catching up. In a vacuum, there's no terminal velocity. On Jupiter with thick atmosphere, terminal velocity is much lower. It's all about the balance.”
Drop Lab
Drop objects of different shapes and masses through fluids of different densities. Race them to find which reaches terminal velocity fastest.
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Drop a sphere and a flat plate of the same mass. The sphere falls faster (lower drag coefficient). Then switch from air to water — terminal velocities plummet!
Shape matters enormously. A streamlined teardrop has Cd ≈ 0.04 while a flat plate has Cd ≈ 1.2. That's a 30× difference in drag! This is why cars and planes are shaped the way they are.