# Transcribed Image Text: (1) Consider a medium with a quadratic drag force Farag = -cv². (a) Find an expression for the

Excerpt
of part (b) in terms of dv/dy, and then use separation of variables to find an expression for v(y), i.e., the upwards velcity as a function of y. Assume the initial upwards speed to be vo and the initial position to be y = 0.

Transcribed Image Text: (1) Consider a medium with a quadratic drag force Farag = -cv².
(a) Find an expression for the terminal velocity vT of a projectile in ts medium.
(b) Show that the equation of motion for vertical motion upwards can be written as
i = -g[1+ (v/vr)³].
(c) As an intermediate step for part (d), use the chain rule of calculus to show that
i = dv/dt can be written as i = v dv/dy.
(d) Use the result from part (c) to write the equation of motion of part (b) in terms
of dv/dy, and then use separation of variables to find an expression for v(y), i.e.,
the upwards velcity as a function of y. Assume the initial upwards speed to be vo
and the initial position to be y = 0.