Asked by ijat
A differential equation governing the velocity v of a falling mass m
to air resistance proportional to the square of the instantaneous velocity is
m dv/dt=mg-kv^2
where k>0 is a constant of proportionality. The positive direction is downward.
(a)Solve the equation subject to initial condition v(0)=v_0.
(b)Determine the limiting velocity.
(c)If the distance s, measured from the point where the mass was released above the ground, is related to velocity by ds/dt=v, find an explicit form of s if s(0)=0.
to air resistance proportional to the square of the instantaneous velocity is
m dv/dt=mg-kv^2
where k>0 is a constant of proportionality. The positive direction is downward.
(a)Solve the equation subject to initial condition v(0)=v_0.
(b)Determine the limiting velocity.
(c)If the distance s, measured from the point where the mass was released above the ground, is related to velocity by ds/dt=v, find an explicit form of s if s(0)=0.