HKDSE Mechanics · Forces & Motion

Skydiving & Terminal Velocity

Watch air resistance grow with speed until the resultant force becomes zero and velocity approaches terminal velocity.

Force F Velocity v Acceleration a Air resistance

3D Descent

W (weight) R (drag) ΣF v a

Skydiver

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Speed v

0.00 m/s

Acceleration a

0.00 m/s²

Resultant ΣF

0.00 N

Height h

3000 m

v–t speed vs time

a–t acceleration vs time

Controls

Teaching preset Mass m (kg): 75 Body posture Effective area A (m²): 0.70 Drag coefficient C_d: 1.00 Exit height h₀ (m): 3000 Auto-open altitude (m): 800 Auto-open parachute at altitude Crosswind (m/s): 0.0 Camera shake (speed feel)

Respects prefers-reduced-motion: shake stays off when the system requests reduced motion.

Live readings

Mass m75 kg

g9.81 m/s²

Weight mg736 N

Air resistance R0 N

Resultant ΣF736 N

Speed v0 m/s

Terminal v_t—

Acceleration a9.81 m/s²

Time t0.00 s

StateReady

HKDSE formula focus

\( R = \tfrac12\,\rho C_d A v^2 \)

\( \Sigma F = mg - R \quad(\text{down}+) \)

\( a = \Sigma F / m \)

\( v_t = \sqrt{\dfrac{2mg}{\rho C_d A}} \)

At terminal velocity, R = mg so ΣF = 0 and a = 0; speed stays nearly constant.

Why heavy ≠ light at v_t

Weight grows with mass (mg), but air resistance depends on shape and speed, not mass. A heavier jumper needs a larger R to balance weight, so equilibrium occurs at a higher terminal speed. Without drag, all masses fall with the same g.

Landing challenge

Choose the challenge preset. Open the parachute in time, fight the crosswind, and land inside the target ring with speed below the safe limit (5 m/s).

Model assumptions

Quadratic drag; constant air density ρ = 1.2 kg/m³
Parachute instantly raises A and C_d when opened
Crosswind is a constant horizontal air-speed for the challenge
No lift; point-mass vertical + horizontal drag model