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(c) The equation of motion for a particle falling under the influence of gravity and a linear drag force is mÿj = mg – by, where m is the particle mass, g is the acceleration due to gravity, b is the coefficient of linear drag, and the vertical coordinate y is taken to have units of meters. (Note: the y-axis points downwards).
dvy (Uter - Vy), dt T where we have set 7 = m/b (a constant with units of time). =
(iv) Using the technique of separation of variables solve the above form of the equation of motion to determine the velocity vy as a function of time. You should use that the particle starts at rest (i.e. vy(t = 0) = 0). (v) What is the velocity of the particle at late times (i.e. for t » 7)? Explain why this result makes sense.
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