# Albert's skydive

**Classical Mechanics**Level 3

In another reality Albert and his friend Bernard are on a plane. Naturally, as most centenarians, they are playful and always ready to fool around. Prankster Bernard pushes Albert out of the plane. While still laughing he states: " Let \(v(t)\) be the speed of Albert at time \(t\) . Without parachute, the change in speed between two instants is given by

\(v\left( t+dt \right) \quad -\quad v(t)\quad =\quad gdt\quad -\quad \mu v(t)dt\) "

where, \(dt\) is an infinitesimal increment of time, \(\mu \) is the friction coefficient resulting from Albert's shape and mass, \(g\) is the acceleration of gravity.

Find \({ v }_{ M }\), the terminal speed, and Evaluate the quantity \(v/{ v }_{ M }\) at \(t \) = 10s.

Data: \(\mu \) = 0.18 \({ s }^{ -1 }\) ; \(g \) = 4.2 \({ m.s }^{ -2 }\) ; \(v(0)={ v }_{ 0 }=0 \ m.{ s }^{ -1 }\) .

Assumptions: \(g \), the acceleration of gravity is considered constant.