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

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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.

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