(Solved): Q8. Consider a body falling from a height \( h \), and suppose that it encounters a resistance pro ...

Q8. Consider a body falling from a height \( h \), and suppose that it encounters a resistance proportional to its velocity. Show that Newton's equation for this system is \( m \frac{d^{2} x}{d t^{2}}=-\gamma \frac{d x}{d t}+m g \quad \) or \( \frac{d v}{d t}+\frac{\gamma}{m} v=g \) where \( \gamma \) is a frictional coefficient. Solve this equation for \( v(t) \), given that its velocity at \( t=0 \) is zero. Show that \( v \) attains a limiting velocity given by \( v_{l i m}=m g / \gamma \). This limiting velocity is called the terminal velocity.