ENADE Física Practice Questions - ENADE Física - Exame Nacional De Desempenho Dos Estudantes Exam

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A projectile of mass $m$ is launched vertically upward from the ground with initial velocity $v_0$ in a viscous medium experiencing linear drag $\vec{F}_{drag} = -b\vec{v}$, where $b > 0$. With gravitational acceleration $g$ directed downward, what is the terminal velocity magnitude $v_{ter}$ during free fall and the velocity function $v(t)$ during upward ascent?

$$v_{ter} = \frac{b}{mg}$ and $v(t) = v_0 e^{-\frac{b}{m}t} - gt$ $$v_{ter} = \sqrt{\frac{mg}{b}}$ and $v(t) = \left(v_0 - \frac{mg}{b}\right)e^{-\frac{b}{m}t} + \frac{mg}{b}$ $$v_{ter} = \frac{mg}{b}$ and $v(t) = \left(v_0 + \frac{mg}{b}\right)e^{-\frac{b}{m}t} - \frac{mg}{b}$ $$v_{ter} = \frac{mg}{b}$ and $v(t) = v_0 \cos\left(\frac{b}{m}t\right) - \frac{mg}{b}\sin\left(\frac{b}{m}t\right)$

Correct Answer:

$$v_{ter} = \frac{mg}{b}$ and $v(t) = \left(v_0 + \frac{mg}{b}\right)e^{-\frac{b}{m}t} - \frac{mg}{b}$

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