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Fundamentals of Differential Equations

An object of mass 5 kg is released from rest 1000 m above

the ground and allowed to fall under the influence of grav-

ity. Assuming the force due to air resistance is proportional

to the velocity of the object with proportionality constant

$$b=50 \mathrm{N}-\mathrm{sec} / \mathrm{m}$$, determine the equation of motion of the

object. When will the object strike the ground?