Exploring the Physics of Rock Climbing and Sky Diving - Nathan Williamson -

Kinematics Concepts  Acceleration is a derivative of Velocity  Velocity is a derivative of Position  Terminal Velocity  Acceleration x Time  Drag Coefficient

Rock Climbing

Skydiving - Reaching Terminal Velocity The SLOPE is the Velocity  65.2 m/s = 148 mph

Parachute Deployment - Velocity Change The AREA =  a dt =  v Max Acc = 3.7 g’s!  Somersaults Final Chute Velocity

Velocity Change From Parachute (14.4g x sec) – (8.3g x sec) = 6.1g x sec  v = (6.1g x sec) x 9.8m/s/s = 59.78m/s Subtract Velocity Change from Terminal Velocity 65.2m/s m/s = 5.42m/s  New Velocity (12 mph) Most of the Terminal Velocity lost when chute deployed Area below 1 gTotal Area vv

Drag Coefficient Force of Drag: F D = -bv 2 where b is the drag coefficient As velocity increases, the magnitude of the resistive force approaches the gravitational force: mg – bv 2 = 0 Therefore, terminal velocity: v T = (mg / b) 1/2 Giving average drag coefficient of: b = mg / v T 2 b = 160kg x 9.8m/s/s / (65.2m/s) 2 = (Total Mass)

Drag Coefficient Typical Drag Coefficients: Single Skydiver – Bicyclist – 0.9 Hummer H2 – 0.57 Ferrari Testarossa – 0.36 Smooth Sphere – 0.1 Learjet 24 – 0.022