where m lbs is its mass and g is the gravitational constant

where m lbs is its mass and g is the gravitational constant. Determine the terminal velocity of the body when m =150 lbs and k = 60 lbs/sec.

Answer: 80 ft/sec

m*dv/dt + kv = mg

Divide all over by m :

dv/dt + (k/m)*v = g

Integrating factor = e^(integral of (k/m)) = e^(kt/m)

Multiply all over by the Integrating factor :

e^(kt/m) * [dv/dt + (k/m)*v = g]

e^(kt/m)*dv/dt + (k/m)*v*e^(kt/m) = g*e^(kt/m)

d/dt(ve^(kt/m)) = g*e^(kt/m)

Integrating both sides :

ve^(kt/m) = Integral of g*e^(kt/m)

ve^(kt/m) = g*(m/k)*e^(kt/m) + C

Divide all over by e^(kt/m) :
v = gm/k + Ce^(-kt/m)

g = 32 , m = 150 , k = 60

For terminal velocity, t ---> infinity :

v = 32*150/60 + e^(-k*infinity/150)

v = 80 + e^(-infinity)
v = 80 + (approx 0)
v = 80

Answer ---> 80 feet/second