A firefighter who weighs 192 lb slides down an infinitely long fire pole that exerts a friction resistive force with magnitude proportional to his speed, with k D 2:5 lb-s/ft. Assuming that he starts from rest, find his velocity as a function of time and find his terminal velocity

Explanation:

Weight of the firefighter, W = 192 lb

W = mg

g = 32 ft/s²

Mass of the firefighter, m = W/g

m = 192/32

m = 6 slugs

k = 2.5 lb-s/ft

The force, F = ma = kv

2.5v = 6a

a = 2.5v/6

a = 5v/12

The fundamental dynamic equation;

dv/dt + drag + gravity = 0

dv/dt = -g-a

dv/dt = -32-5v/12..............(a)

The motion will attain terminal velocity when dv/dt = 0

-32 - 5v/12 = 0

-32 = 5v/12

-384 = 5v

v₀ = -384/5

v₀ = -384/5

dv/dt = -32 - 5v/12

Take exponential of both sides

c = v₀ = -384/5

grav potential energy