# Albert's skydive

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.

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