A differential equation for the velocity of a falling mass subjected to air resistance proportional to the square of the instantaneous velocity is m(dv/dt)=mg-kv2 Where ? > 0 is a constant of proportionality. The positive direction is downward. (a) Solve the equation subject to the initial condition ?(0) = ?0 . (b) Use the solution in part (a) to determine the terminal velocity of the mass. (c) If the distance s, measured from the point where the mass was released above ground, is related to velocity v by ds/dt=v(t) , find an explicit expression for s(t) if s(0)=0

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.